ORIGINAL_ARTICLE
An investigation on regular relations of universal hyperalgebras
In this paper, by considering the notion of $\Sigma$-hyperalgebras for an arbitrary signature $\Sigma$, we study the notions of regular and strongly regular relations on a $\Sigma$-hyperalgebra, $\mathfrak{A}$. We show that each regular relation which contains a strongly regular relation is a strongly regular relation. Then we concentrate on the connection between the fundamental relation of $\mathfrak{A}$ and the set of complete parts of $\mathfrak{A}$.
https://as.yazd.ac.ir/article_1171_ee37ba41304093beaa74969ad5e9db30.pdf
2018-02-01
1
21
10.22034/as.2018.1171
Universal algebras
Regular relation
Fundamental relation
Complete part
S.
Rasouli
1
Department of Mathematics, Persian Gulf University, Bushehr, 75169, Iran
AUTHOR
B.
Davvaz
2
Department of Mathematics Yazd University Yazd, Iran
LEAD_AUTHOR
[1] G. Birkhoff, Lattice Theory, 3rd edition. Colloq. Publ., vol. 25, Amer. Math. Soc., Providence, (1967).
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[2] P. Corsini, Contributo alla teoria degli ipergruppi, Atti Soc. Pelor. Sc. Mat. Fis. Nat. Messina, Messina, Italy, (1980), pp. 1-22.
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[3] P. Corsini and V. Leoreanu, Applications of Hyperstructure Theory, Kluwer, Dordrecht, (2003).
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[4] B. Davvaz and V. Leoreanu-Fotea, Hyperring Theory and Applications, International Academic Press, USA, (2007).
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[5] B. Davvaz and T. Vougiouklis, n-ary hypergroups, Iran. J. Sci. Technol. Trans. A Sci., 30(2) (2006), 165-174.
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[6] B. Davvaz and W. A. Dudek. S. Mirvakili, Neutral elements, fundamental relations and n-ary hypergroups, Internat. J. Algebra Comput., 19(4) (2009), 567-583.
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dependent choice, Algebra Universalis, 13 (1981), 69-77.
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[15] M. Koskas, Groupoids, demi-hypergroupes et hypergroupes, J. Math. Pures Appl., 49(9) (1970), 155-192.
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[16] V. Leoreanu-Fotea and B. Davvaz, n-hypergroups and binary relations, European J. Combinatorics, 29 (2008), 1207-1218.
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[17] V. Leoreanu-Fotea, Contributions to the study of the heart of a hypergroup, Doctoral Thesis: Babes-Bolyai University, Cluj-Napoca, Romania, (1998).
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[18] F. Marty, Surune generalization de la notion de groupe, 8th Congress Math. Scandenaves, Stockholm, (1934) 45-49.
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[19] R. Migliorato, On the complete hypergroups, Rivista diMatematica Pura ed Applicata, 14 (1994), 21-32.
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[20] C. Pelea, On the fundumental relation of a multialgebra, Ital. J. Pure Appl. Mat., 10 (2001), 327-342.
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[22] C. Pelea and I. Purdea, Multialgebras, universal algebras and identities, J. Aust. Math. Soc., 81 (2006), 121-139.
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[23] H. E. Pickett, Homomorphisms and subalgebras of multialgebras, Pacic J. Math., 21 (1967), 327-342.
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[24] S. Rasouli and B. Davvaz, Lattices derived from hyperlattices, Comm. Algebra, 38(8) (2010), 2720-2737.
25
[25] S. Rasouli and B. Davvaz, Construction and spectral topology on hyperlattices, Mediterr. J. Math., 7 (2010), 249-262.
26
[26] S. Rasouli and B. Davvaz, Homomorphism, ideals and binary relations on hyper-MV algebras, J. of Mult-Valued Logics & Soft Computing, 17 (2011), 47-68.
27
[27] S. Rasouli, D. Heydari and B. Davvaz, eta-relations and transitivity conditions of eta on hyper-MV algebras, J. of Mult-Valued Logics & Soft Computing, 15 (2009), 517-524.
28
[28] S. Rasouli, D. Heydari and B. Davvaz, relations and transitivity conditions of on hyper-BCK algebras, Hacettepe Journal of Mathematics and Statistics, 39(4) (2010), 461-469.
29
[29] S. Rasouli, D. Heydari and B. Davvaz, An investigation on homomorphisms and subhyperalgebras of hyperalgebras, Hacettepe Journal of Mathematics and Statistics, 43(6) (2014), 971-984.
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[30] D. Schweigert, Congruence relations of multialgebras, Discrete Math., 53 (1985), 249-253.
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[31] Y. Sureau, Contribution a la thorie des hypergroupes ethypergroupes operant transivement sur un ensemble,
32
Doctoral Thesis, (1980).
33
ORIGINAL_ARTICLE
An efficient algorithm for Mixed domination on Generalized Series-Parallel Graphs
A mixed dominating set $S$ of a graph $G=(V, E)$ is a subset of vertices and edges like $S \subseteq V \cup E$ such that each element $v\in (V \cup E) \setminus S$ is adjacent or incident to at least one element in $S$. The mixed domination number $\gamma_m(G)$ of a graph $G$ is the minimum cardinality among all mixed dominating sets in $G$. The problem of finding $\gamma_{m}(G)$ is known to be NP-complete. In this paper, we present an explicit polynomial-time algorithm using the parse tree to construct a mixed dominating set of size $\gamma_{m}(G)$ where $G$ is a generalized series-parallel graph.
https://as.yazd.ac.ir/article_1208_a3d01b0ef81b9ace16f3dc16a272884d.pdf
2018-02-01
23
39
10.22034/as.2018.1208
Mixed Dominating Set
Generalized Series-Parallel
Parse Tree
Tree-width
M.
Rajaati
1
Department of Computer Science, Yazd University, Yazd, Iran.
AUTHOR
M.R.
Hooshmandasl
2
Department of Computer Science, Yazd University, Yazd, Iran.
LEAD_AUTHOR
A.
Shakiba
3
Department of Computer Science, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
AUTHOR
P.
Sharifani
4
Department of Computer Science, Yazd University, Yazd, Iran.
AUTHOR
M.J.
Dinneen
5
Department of Computer Science, The University of Auckland, Auckland, New Zealand.
AUTHOR
[1] G. S. Adhar, S. Peng, Mixed domination in trees: a parallel algorithm, Congr. Numer. 100 (1994) 73-80.
1
[2] Y. Alavi, M. Behzad, L. M. Lesniak-Foster, E. Nordhaus, Total matchings and total coverings of graphs, J. Graph Theory 1(2) (1977) 135-140.
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[3] Y. Alavi, J. Liu, J. Wang, Z. Zhang, On total covers of graphs, Discrete Math. 100 (1992) 229-233.
3
[4] P. Chebolu, M. Cryan, R. Martin, Exact counting of Euler tours for generalized series-parallel graphs, J. Discrete Algorithms 10 (2012) 110-122.
4
[5] T. W. Haynes, S. Hedetniemi, P. Slater, Fundamentals of domination in graphs, CRC Press, 1998.
5
[6] T. W. Haynes, S. Hedetniemi, P. Slater, Domination in graphs: advanced topics, Taylor & Francis, 1998.
6
[7] S. M. Hedetniemi, S. T. Hedetniemi, R. Laskar, A. McRae, A. Majumdar, Domination, independence and irredundance in total graphs: a brief survey, Graph Theory, Combinatorics and Applications: Proceedings of the 7th Quadrennial International Conference on the Theory and Applications of Graphs 2 (1995) 671-683.
7
[8] J. E. Hopcroft, R. E. Tarjan, Dividing a graph into triconnected components, SIAM J. Comput. 2(3) (1973) 135-158.
8
[9] T. Kikuno, N. Yoshida,Y. Kakuda, A linear algorithm for the domination number of a series-parallel graph, Discrete Appl. Math. 5(3) (1983) 299-311.
9
[10] J. K. Lan, G. J. Chang, On the mixed domination problem in graphs, Theoret. Comput. Sci. 476(84) (2013) 84-93.
10
[11] A. Majumdar, Neighborhood Hypergraphs: A Framework for Covering and Packing Parameters in Graphs, PhD thesis,
11
Clemson University, Department of Mathematical Sciences, South Carolina, 1992.
12
[12] D. F. Manlove, On the algorithmic complexity of twelve covering and independence parameters of graphs, Discrete Appl. Math. 91(1) (1999) 155-175.
13
[13] M. Rajaati, M. R. Hooshmandasl, M. J. Dinneen, A. Shakiba, On fixed-parameter tractability of the mixed domination problem for graphs with bounded tree-width, Discrete Math. Theor. Comput. Sci. 20(2) (2018) 1-25.
14
[14] D. B. West, Introduction to graph theory, Prentice Hall Upper Saddle River, 2001.
15
[15] Y. Zhao, L. Kang, M. Y. Sohn, The algorithmic complexity of mixed domination in graphs, Theoret. Comput. Sci.
16
412(22) (2011) 2387-2392.
17
ORIGINAL_ARTICLE
A short Note on prime submodules
Let $R$ be a commutative ring with identity and $M$ be a unital $R$-module. A proper submodule $N$ of $M$ with $N:_RM=\frak p$ is said to be prime or $\frak p$-prime ($\frak p$ a prime ideal of $R$) if $rx\in N$ for $r\in R$ and $x\in M$ implies that either $x\in N$ or $r\in \frak p$. In this paper we study a new equivalent conditions for a minimal prime submodules of an $R$-module to be a finite set, whenever $R$ is a Noetherian ring. Also we introduce the concept of arithmetic rank of a submodule of a Noetherian module and we give an upper bound for it.
https://as.yazd.ac.ir/article_1209_0c73ba791d9609f1a9176263ae0fbd5b.pdf
2018-02-01
41
49
10.22034/as.2018.1209
arithmetic rank of a submodule
associated primes
height of a prime submodule
minimal prime submodule
prime submodule
Jafar
A&#;zami
1
Department of mathematics, Faculty of sciences, University of Mohaghegh Ardabili, Ardabil, Iran.
LEAD_AUTHOR
[1] S. Abu-Saymeh, On dimensions of nitely generated modules, Comm. Alg. 23(1995), 1131-1144.
1
[2] J. Azami and M. Khajepour, Topics in prime submodules and other aspects of the prime avoidence theorem, Preprint(Mathematical Reports) .
2
[3] K. Bahmanpour, A. Khojali and R. Naghipour, A note on minimal prime divisors of an ideal, Algebra Colloq. 18(2011), 727-732.
3
[4] M. Behboodi, A generalization of the classical Krull dimension for modules, J. Algebra. 305(2006), 1128-1148.
4
[5] W. Bruns and J. Herzog, Cohen-Macaulay Rings, Cambridge Univ. Press, Cambridge, UK, 1993.
5
[6] J. Dauns, Prime modules, J. Reine Anegew. Math. 298(1978), 156-181.
6
[7] J. Jenkins and P. F. Smith, On the prime radical of a module over commutative ring, Comm. Alg. 20(1992), 3593-3602.
7
[8] O. A. S. Karamzadeh, The Prime Avoidance Lemma revisited, Kyungpook Math. J. 52(2012), 149-153.
8
[9] C. P. Lu, Unions of prime submodules, Houston J. Math. 23, no.2(1997), 203-213.
9
[10] K. H. Leung and S. H. Man, On commutative Noetherian rings which satisfy the radical formula, Glasgow math. J. 39(1997), 285-293.
10
[11] S. H. Man and P. F. Smith, On chains of prime submodules, Israel J. Math. 127(2002), 131-155.
11
[12] A. Marcelo and J. Munoz Maque, Prime submodules, the discent invariant, and modules of nite length, J. Algebra 189(1997), 273-293.
12
[13] H. Matsumura, Commutative ring theory, Cambridge Univ. Press, Cambridge, UK, 1986.
13
[14] R. L. McCasland and P. F. Smith, Prime submodules of Noetherian modules, Rocky Mountain J. Math. 23(1993), 1041-1062.
14
[15] A. A. Mehrvarz, K. Bahmanpour and R. Naghipour, Arithmetic rank, cohomological dimension and lterregular sequences, J. Alg. Appl. 8(2009), 855-862.
15
[16] J. J. Rotman, An introduction to homological algebra, Pure Appl. Math., Academic Press, New York, 1979.
16
[17] D. Pusat-Yilmaz and P. F. Smith, Chain conditions in modules with krull dimension, Comm. Alg. 24(13)(1996), 4123-4133.
17
ORIGINAL_ARTICLE
Boolean center of lattice ordered $EQ$-algebras with bottom element
In this paper, some new properties of $EQ$-algebras are investigated. We introduce and study the notion of Boolean center of lattice ordered $EQ$-algebras with bottom element. We show that in a good $\ell EQ$-algebra $E$ with bottom element the complement of an element is unique. Furthermore, Boolean elements of a good bounded lattice $EQ$-algebra are characterized. Finally, we obtain conditions under which Boolean center of an $EQ$-algebra $E$ is the subalgebra of $E$.
https://as.yazd.ac.ir/article_1210_746371f11fda39097a765404e37a9111.pdf
2018-02-01
51
68
10.22034/as.2018.1210
$EQ$-algebra
$blEQ$-algebra
Boolean element
Neda
Mohtashamnia
1
Departement of Mathematics, Kerman Branch, Islamic Azad university, Kerman,Iran.
AUTHOR
Lida
Torkzadeh
ltorkzadeh@yahoo.com
2
Departement of Mathematics, Kerman Branch, Islamic Azad university, Kerman,Iran.
LEAD_AUTHOR
[1] C.C. Chang, Algebraic analysis of many valued logics, Trans Am Math Soc 88 (1958) 467-490.
1
[2] M. El-Zekey, Representable good EQ-algebras, Soft Computing, 14 (2010) 1011-1023.
2
[3] M. El-Zekey, V. Novak, R. Mesiar, On good EQ-algebras, Fuzzy sets and systems, 178 (2011) 1-23.
3
[4] F. Esteva, L. Godo, Monoidal t-norm based logic: towards a logic for left-continuous t-norms, Fuzzy SetsSystems, 124 (2001) 271-288.
4
[5] G. Georgescu, L. Leustean, C. Muresan, Maximal residuated lattices with lifting Boolean center, Algebra Universalis (2010) 63(1) 83-99.
5
[6] J. Gispert, A. Torrens, Boolean representation of bounded BCK-algebras, Soft Comput 12 (2008) 941-954.
6
[7] N. Mohtashamnia, L. Torkzadeh, The lattice of prelters of an EQ-algebra, Fuzzy Sets and Systems, 311 (2017) 86-98.
7
[8] P. Hajek, Metamathematics of Fuzzy Logic, Kluwer, Dordrecht (1998).
8
[9] L. Z. Liu, K.T. Li, R0-algebras and weak dually residuated lattice ordered semigroups, Czech Math J, 56 (2006) 339-348.
9
[10] V. Novak, EQ-algebras:primary concepts and properties, in: Proc. Czech-Japan Seminar, Ninth Meeting. Kitakyushu and Nagasaki, Graduate School of Information, Waseda University, August (2006) 18-22.
10
[11] V. Novak, B. De Baets, EQ-algebra, Fuzzy sets and systems, 160 (2009) 2956-2978.
11
[12] L. A. Zadeh, Is there a need for fuzzy logic? Inform Science, 178 (2008) 2751-2779.
12
[13] H. J. Zhou and B. Zhao, Stone-like representation theorems and three-valued letters in R0-algebras (nilpotent minimum algebras), Fuzzy Sets Systems, 162 (2011) 1-26.
13
ORIGINAL_ARTICLE
On endo-semiprime and endo-cosemiprime modules
In this paper, we study the notions of endo-semiprime and endo-cosemiprime modules and obtain some related results. For instance, we show that in a right self-injective ring $R$, all nonzero ideals of $R$ are endo-semiprime as right (left) $R$-modules if and only if $R$ is semiprime. Also, we prove that both being endo-semiprime and being are Morita invariant properties.
https://as.yazd.ac.ir/article_1211_7708ce7a15d1e37878a47603f0c774c7.pdf
2018-02-01
69
80
10.22034/as.2018.1211
Endo-prime modules
endo-semiprime modules
endo-coprime modules
endo-cosemiprime modules
Parvin
Karimi Beiranvand
karimi.pa@fs.lu.ac.ir.
1
Department of mathematics, Lorestan university,P.O.Box 465, Khoramabad, Iran.
AUTHOR
Reza
Beyranvand
2
Department of mathematics, Lorestan university, P.O.Box 465, Khoramabad, Iran.
LEAD_AUTHOR
[1] M. Behboodi and S. H. Sojaee, On chains of classical prime submodules and dimensions theory of modules, Bull. Iranian Math. Society, 36(1) (2010), 149-166.
1
[2] S. Ceken, M. Alkan and P. F. Smith, Second modules over noncommutative rings, Comm. Algebra, 41 (2013), 83-98.
2
[3] J. Dauns, Prime modules, J. Reine Angew. Math., 298 (1978), 156-181.
3
[4] A. Ghorbani, Co-epi-retractable modules and co-pri rings, Comm. Algebra, 38 (2010), 3589-3596.
4
[5] A. Haghany and M. R. Vedadi, Endoprime modules, Acta Math. Hungar., 106(1-2) (2005), 89-99.
5
[6] B. Sarac, On semiprime submodules, Comm. Algebra, 37(7) (2009), 2485-2495.
6
[7] R. Wisbauer, Foundations of module and ring theory, Gordon and Breach Science Publishers Reading (1991).
7
[8] S. Yassemi,The dual notion of prime submodules, Arch. Math. Brno., 37 (2001), 273-278.
8
ORIGINAL_ARTICLE
On dual of the generalized splitting matroids
Given a binary matroid $M$ and a subset $T\subseteq E(M)$, Luis A. Goddyn posed a problem that the dual of the splitting of $M$, i.e., ($(M_{T})^{*}$) is not always equal to the splitting of the dual of $M$, ($(M^{*})_{T}$). This persuade us to ask if we can characterize those binary matroids for which $(M_{T})^{*}=(M^{*})_{T}$. Santosh B. Dhotre answered this question for a two-element subset $T$. In this paper, we generalize his result for any subset $T\subseteq E(M)$ and exhibit a criterion for a binary matroid $M$ and subsets $T$ for which $(M_{T})^{*}$ and $(M^{*})_{T}$ are the equal. We also show that there is no subset $T\subseteq E(M)$ for which, the dual of element splitting of $M$, i.e., ($(M^{'}_{T})^{*}$) equals to the element splitting of the dual of $M$, (($M^{*})^{'}_{T}$).
https://as.yazd.ac.ir/article_1213_5cd3e29998682a9da665160814771b1c.pdf
2018-02-01
81
88
10.22034/as.2018.1213
Binary matroid
dual of a matroid
n-connected matroid
splitting operation
cocircuit
Ghodrat
Ghafari
gh.ghafari@urmia.ac.ir
1
Department of Mathematics, Urmia University, Urmia, Iran
LEAD_AUTHOR
Ghodratollah
Azadi
gh.azadi@urmia.ac.ir
2
Department of Mathematics, Urmia University, Urmia, Iran
AUTHOR
Habib
Azanchiler
h.azanchiler@urmia.ac.ir
3
Department of Mathematics, Urmia University, Urmia, Iran
AUTHOR
[1] S. B. Dhotre, A note on the dual of the splitting matroid, Lobachevskii J. Math., 33, (2012), 229-231.
1
[2] H. Fleischner, Eulerian Graphs and Related Topics, North Holland, Amsterdam, (1990).
2
[3] J. G. Oxley, Matroid Theory, Oxford university press, New York, (2011).
3
[4] T. T. Raghunathan, M. M. Shikare and B. N. Waphare, Splitting in a binary matroid, Discrete math., 184, (1998), 267-271.
4
[5] M. M. Shikare, Gh. Azadi, Determination of the bases of a splitting matroid, European J. combin., 24, (2003), 45-52.
5
[6] M. M. Shikare, Gh. Azadi, B. N. Waphare, Generalized splitting operation and its application, J. Indian. Math. Soc., 78, (2011), 145-154.
6
[7] P. J. Slater, A classsication of 4-connected graphs , J. Combin. Theory, 17, (1974), 281-298.
7
[8] D. J. A. Welsh, Eulerian and bipartite matroids, J. Comb. Theory, 6, (1969), 375-377.
8