ORIGINAL_ARTICLE
HX-hypergroups associated with the direct products of some ${\bf Z}/n {\bf Z}$
One studies the $HX$-hypergroups, corresponding to the Chinese hypergroups associated with the direct products of some ${\bf Z}/n {\bf Z},$ calculating their fuzzy grades.
http://as.yazd.ac.ir/article_835_1f23c85a508ef75b7ad85d4301624c32.pdf
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2018-06-19T11:23:20
1
15
$HX$-group
Fuzzy grade
Piergiulio
Corsini
true
1
University of Udine
University of Udine
University of Udine
LEAD_AUTHOR
[1] R. Ameri, M.M. Zahedi, Hypergroup and join space induced by a fuzzy subset, PU.M.A., (1997) vol. 8,
1
[2] P. Cosini, On Chinese hyperstructures, J. Discrete Math. Sci and Cryptography, Vol 6 (2003), no 2-3,
2
[3] P. Corsini, Join Spaces, Power Sets, Fuzzy Sets, Proc. Fifth International Congress on A.H.A., 1993, Iasi,
3
[4] P. Corsini, A new connection between hypergroups and fuzzy sets, Southeast Bulletin of Math., 27 (2003)
4
[5] P. Corsini, Hyperstructures associated with ordered sets, Bull. the Greek Math. Soc., vol. 48, (2003) 7-18.
5
[6] P. Corsini, Join Spaces, multivalued functions and soft sets, Proc. Int. Conf. Alg. 2010, (ICA 2010),
6
Universitas Gadjah Mada and the Southeast Asian Math.
7
[7] P. Corsini, HX-groups and Hypergroup, Analele Univ. "Ovidius", Math. Series n. 3, (2016).
8
[8] P. Corsini, Hypergroups associated with HX- groups, accepted by Analele Univ. "Ovidius", 2016.
9
[9] P. Corsini, Prolegomena of Hypergroup Theory, Aviani Editore, (1993).
10
[10] P. Corsini, I. Cristea, Fuzzy grade of i.p.s. hypergroups of order less or equal to 6, PU.M.A., vol. 14, no.
11
4, (2003) 275-288.
12
[11] P. Corsini, I. Cristea, Fuzzy grade of i.p.s. hypergroups of order 7, Iran J. of Fuzzy Systems, 1 (2004)
13
[12] P. Corsini, I. Cristea, Fuzzy sets and non complete 1-hypergroups, An. St. Univ. Ovidius Constanta, 13
14
(1) (2005) 27-54.
15
[13] P. Corsini and B. Davvaz, New connections among multivalued functions, hyperstructures and fuzzy sets,
16
J. Journal Math. Stat., (JJMS) 3 (3) (2010) 133- - 150.
17
[14] P. Corsini and V. Leoreanu-Fotea, Join Spaces associated with Fuzzy Sets, J. Combin. Inform. Sys. Sci.,
18
vol. 20, n. 1 (1995) 293-303.
19
[15] P. Corsini, V. Leoreanu, Applications of Hyperstructure Theory, Advances in Mathematics, Kluwer Aca-
20
demic Publishers, (2003).
21
[16] P. Corsini and V. Leoreanu-Fotea, On the grade of a sequence of fuzzy sets and join spaces determined
22
by a hypergraph, Southeast Asian Bull. Math., 34 (2010) 113-119.
23
[17] P. Corsini, V. Leoreanu-Fotea, A. Iranmanesh, On the sequence of join spaces and membership functions
24
determined by a hypergraph, J. Mult. Logic Soft Comput., vol. 14, issue 6, (2008) 565-577.
25
[18] P. Corsini, V. Leoreanu-Fotea, A.M. Lepellere, Fuzzy grade of some hyperstructures, Int. J. Alg. Hyper-
26
struc. Appl., no. 2, Tehran, Iran
27
[19] P. Corsini and R. Mahjoob, Multivalued functions, fuzzy subsets and join spaces, Ratio Mathematica, 20
28
(2010) 1-41.
29
[20] I. Cristea, A property of the connection between fuzzy sets and hypergroupoids, Italian J. Pure Appl.
30
Math., 21 (2007) 73-82.
31
[21] B. Davvaz, Hypergroups and fuzzy sets, Proc. 4th Seminar on Fuzzy Sets and it's Applications, University
32
of Mazandaran, Babolsar, Iran, (2003), 45-54.
33
[22] F. Yuming Algebraic hyperstructures obtained from algebraic structures with binary fuzzy binary relations,
34
Italian J. Pure Appl. Math., 25 (2009) 49.
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[23] S. Hoskova, P. Chvalina, C. Rackova, Noncommutative join spaces of integral operators and related hy-
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perstructures, Advances MT, 1 (2000) 7-24.
37
[24] L. Hongxing, D. Qinzhi and W. Peizhuang, Hypergroup (I). Busefal, Vol. 23, (1985)
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[25] L. Hongxing, W. Peizhuang, Hypergroup Busefal, (II), vol. 25, (1986).
39
[26] L. Hongxing, HX-Groups, Busefal, Vol. 33, (1987).
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[27] M. Honghai, Uniform HX-groups, Busefal Vol. 47, (1991).
41
[28] A. Maturo, I. Tofan, Iperstrutture, strutture fuzzy ed applicazioni, monograa di 168 pagine, pubblicazione
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nanziata con i fondi del progetto internazionale Socrates-Erasmus 2000/2001, Italia-Romania, Dierre
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Edizioni San Salvo, agosto.
44
[29] W. Prenowitz, J. Jantosciak, Join Geometries, Springer-Verlag UTM, (1979).
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[30] S. J. Rasovic, Hyperrings constructed by multiendomorphisms of hypergroups, Proceedings of the 10th
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International Congress on AHA, Brno, (2008)
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[31] K. Seramidis, A. Kehagias, M. Konstantinidou, The L-fuzzy Corsini join hyperoperation, Italian Journal
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of Pure and Applied Mathematics, 12 (2003).
49
[32] S. Spartalis, The hyperoperation relation and the Corsini's partial or not partial hypergroupoid, Italian J.
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Pure Appl. Math., 24 (2008) 97{112.
51
[33] M. Stefanescu, I. Cristea, On the fuzzy grade of hypergroups, Fuzzy Sets and Systems, 159 (2008).
52
[34] T. Vougiouklis Hyperstructures and their representations, Hadronic Press Inc. (1994).
53
[35] M. Yavari, Corsini's method and construction of join spaces, Italian J. Pure Appl. Math., 23 (2008)
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[36] Z. Zhenliang, The properties of HX-Groups, Italian J. Pure Appl. Math., Vol. 2, (1997).
55
[37] Z. Zhenliang, Classications of HX-Groups and their chains of normal subgroups, Italian J. Pure Appl.
56
Math., Vol. 5, (1999).
57
[38] Z. Baojie, L. Hongxing, HX-type Chaotic (hyperchaotic) System Based on Fuzzy Inference Modeling,
58
Italian J. Pure Appl. Math., to appear.
59
ORIGINAL_ARTICLE
A note on the order graph of a group
The order graph of a group $G$, denoted by $\Gamma^*(G)$, is a graph whose vertices are subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $|H|\big{|}|K|$ or $|K|\big{|}|H|$. In this paper, we study the connectivity and diameter of this graph. Also we give a relation between the order graph and prime graph of a group.
http://as.yazd.ac.ir/article_875_0edfd6e49270d69dbf1f6ea8948e0b59.pdf
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17
24
Connected graph
Frobenius group
Order graph
Prime graph
Hamid Reza
Dorbidi
hr_dorbidi@yahoo.com
true
1
University of Jiroft
University of Jiroft
University of Jiroft
LEAD_AUTHOR
[1] J. A. Bondi, J. S. Murty, Graph theory with applications, American Elsevier Publishing Co, INC, 1997.
1
[2] Y. Chen, On Thompson’s conjecture, J. Algebra 15 (1996), 184-193.
2
[3] J. A. Gallian, Contemporary Abstract Algebra, D. C. Heath and company, 1994.
3
[4] B. Huppert, Character Theory of Finite Groups, De Gruyter Expositions in Mathematics, New York 1998.
4
[5] Sh. Payrovi, H. Pasebani, The Order Graphs of Groups, J Algebraic Structures and Their Applications, 1
5
(no 1) ( 2014 ), 1-10.
6
[6] J. S. Wiliams, Prime Graph Components of Finite Groups, J. Algebra 69 (1981), 487-513.
7
ORIGINAL_ARTICLE
Exact sequences of extended $d$-homology
In this article, we show the existence of certain exact sequences with respect to two homology theories, called d-homology and extended d-homology. We present sufficient conditions for the existence of long exact extended d- homology sequence. Also we give some illustrative examples.
http://as.yazd.ac.ir/article_886_e041c7772dac1fb8eb2e2a396ea1a011.pdf
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25
38
kernel
image
abelian category
standard homology
(extended) d-homology
exact sequence
Mohammad Zaher
Kazemi Baneh
zaherkazemi@uok.ac.ir
true
1
University of Kurdistan
University of Kurdistan
University of Kurdistan
LEAD_AUTHOR
Seyed Naser
Hosseini
nhoseini@uk.ac.ir
true
2
Shahid Bahonar University of Kerman
Shahid Bahonar University of Kerman
Shahid Bahonar University of Kerman
AUTHOR
[1] F. Borceux, D. Bourn, MalCev, Protomodular, Homological and Semi-Abelian Categories, Kluwer Academic
1
Publishers, 2004.
2
[2] S.N. Hosseini, M.Z.Kazemi Baneh, Homology with respect to a Kernel Transformation, Turk. J. Math. 35
3
(2011), 169-186.
4
[3] M.Z. Kazemi-Baneh,Homotopic Chain Maps Have Equal s-Homology and d-Homology, Int. J. Math. Math.
5
Sci., Volume 2016, 2016.
6
[4] M.Z. Kazemi Baneh, Homotopic chaim maps have equal extended d-Homology, 47th Annual Iranian Mathematics Conference, Kharazmi University, Aug. 2016.
7
[5] S. MacLane, Categories for the Working Mathematician, 2nd edition, Springer-Verlag, 1998.
8
[6] M.S. Osborne, Basic Homological Algebra, Springer-Verlag, 2000.
9
ORIGINAL_ARTICLE
The principal ideal subgraph of the annihilating-ideal graph of commutative rings
Let $R$ be a commutative ring with identity and $\mathbb{A}(R)$ be the set of ideals of $R$ with non-zero annihilators. In this paper, we first introduce and investigate the principal ideal subgraph of the annihilating-ideal graph of $R$, denoted by $\mathbb{AG}_P(R)$. It is a (undirected) graph with vertices $\mathbb{A}_P(R)=\mathbb{A}(R)\cap \mathbb{P}(R)\setminus \{(0)\}$, where $\mathbb{P}(R)$ is the set of proper principal ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if $IJ=(0)$. Then, we study some basic properties of $\mathbb{AG}_P(R)$. For instance, we characterize rings for which $\mathbb{AG}_P(R)$ is finite graph, complete graph, bipartite graph or star graph. Also, we study diameter and girth of $\mathbb{AG}_P(R)$. Finally, we compare the principal ideal subgraph $\mathbb{AG}_P(R)$ and spectrum subgraph $\mathbb{AG}_s(R)$.
http://as.yazd.ac.ir/article_888_2d482e44ddd64c95a532eea7ca73b7f8.pdf
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39
52
commutative rings
annihilating-ideal
principal ideal
graph
Reza
Taheri
true
1
Islamic Azad University, Science and Research Branch, Tehran, Iran
Islamic Azad University, Science and Research Branch, Tehran, Iran
Islamic Azad University, Science and Research Branch, Tehran, Iran
AUTHOR
Abolfazl
Tehranian
tehranian1340@yahoo.com
true
2
Islamic Azad University, Science and Research Branch, Tehran, Iran
Islamic Azad University, Science and Research Branch, Tehran, Iran
Islamic Azad University, Science and Research Branch, Tehran, Iran
LEAD_AUTHOR
[1] G. Aalipour, S. Akbari, M. Behboodi, R. Nikandish and M. J. Nikmehr and F. Shahsavari, The classification of the annihilating-ideal graph of a commutative ring, Algebra Colloquium 21 (2014) 249-256.
1
[2] G. Aalipour, S. Akbari, R. Nikandish, M. J. Nikmehr and F. Shahsavari, On the coloring of the annihilating-ideal graph of a commutative ring, Discrete Math. 312 (2012) 2620-2626.
2
[3] G. Aalipour, S. Akbari, R. Nikandish, M. J. Nikmehr and F. Shahsavari, Minimal prime ideals and cycles in
3
annihilating-ideal graphs, Rocky Mountain J. Math. 5 (2013) 1415-1425.
4
[4] F. Aliniaeifard and M. Behboodi, Rings whose annihilating-ideal graphs have positive genus, J. Algebra Appl. 11, 1250049 (2012) [13 pages] DOI: 10.1142/S0219498811005774.
5
[5] F. Aliniaeifard, M. Behboodi, E. Mehdi-Nezhad, and A.M. Rahimi, On the diameter and girth of an annihilating-ideal graph, to apear.
6
[6] F. Aliniaeifard, M. Behboodi, E. Mehdi-Nezhad and A. M. Rahimi, The annihilating-ideal graph of a commutative ring with respect to an ideal, Commun. Algebra 42 (2014) 2269-2284.
7
[7] D. F. Anderson and A. Badawi, The total graph of a commutative ring, J. Algebra 320 (2008) 2706-2719.
8
[8] D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 217 (1999) 434-447.
9
[9] L. Anderson, A First Course in Discrete Mathematice, Springer Undergraduate Mathematics Series,2000.
10
[10] M. Baziar, E. Momtahan and S. Safaeeyan, A zero-divisor graph for modules with respect to their (first) dual, J. Algebra Appl. 12, 1250151 (2013) [11 pages] DOI: 10.1142/S0219498812501514.
11
[11] M. Behboodi, Zero divisor graphs for modules over commutative rings, J. Commut. Algebra 4 (2012) 175-197.
12
[12] M. Behboodi, Z. Rakeei,The annihilating-ideal graph of commutative rings I, J. Algebra Appl. 10 (2011) 727-739.
13
[13] M. Behboodi, Z. Rakeei,The annihilating-ideal graph of commutative rings II, J. Algebra Appl. 10 (2011) 740-753.
14
[14] I. Chakrabarty, S. Ghosh, T. K. Mukherjee and M. K. Sen, Intersection graphs of ideals of rings, Discrete Math. 309 (2009), 5381-5392.
15
[15] W. K. Nicholson and E. s , anchez-Campos, Rings with the dual of the isomorphism theorem , J. Algebra 271 (1) (2004), 391-406.
16
[16] R. Nikandish and H. R. Maimani, Dominating sets of the annihilating-ideal graphs, Electronic Notes in Discrete Math. 45 (2014) 17-22.
17
[17] R. Y. Sharp, Steps in commutative algebra Cambridge University Press, Cambridge, 1991.
18
[18] R. Taheri, M. Behboodi and A. Tehranian, The spectrum subgraph of the annihilating-ideal graph of a commutative ring, J. Algebra Appl. 14 (2015) [19 page].
19
ORIGINAL_ARTICLE
The concept of logic entropy on D-posets
In this paper, a new invariant called {\it logic entropy} for dynamical systems on a D-poset is introduced. Also, the {\it conditional logical entropy} is defined and then some of its properties are studied. The invariance of the {\it logic entropy} of a system under isomorphism is proved. At the end, the notion of an $ m $-generator of a dynamical system is introduced and a version of the Kolmogorov-Sinai theorem is given.
http://as.yazd.ac.ir/article_900_22873ec50d4c1ad74a344a74ff1e040d.pdf
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53
61
D-poset
logic entropy
dynamical system
isomorphism
$ m $-generator
Uosef
Mohammadi
u.mohamadi@ujiroft.ac.ir
true
1
University of Jiroft
University of Jiroft
University of Jiroft
LEAD_AUTHOR
[1] G. Birkhoff, J. Von Neumann, The logic of quantum mechanics, Ann. Math. 37, 823–842 (1936).
1
[2] M. Ebrahimi, B. Mosapour, The concept of entropy on D-posets, Cankaya University Journal of Science and Engineering, 10, 137–151 (2013).
2
[3] F. Kopka and F. Chovanec, D-posets, Mathematica Slovaca 44, 21–34 (1994).
3
[4] T. Kroupa, Conditional probability on MV-algebras, Fuzzy Sets and Systems. 369–381 (2005).
4
[5] U. Mohammadi, Weighted entropy function as an extension of the Kolmogorov-Sinai entropy, U. P. B. Sci. Series A, no. 4, 117–122 (2015).
5
[6] U. Mohammadi, Relative entropy functional of relative dynamical systems, Cankaya University Journal of Science and Engineering, no. 2, 29–38 (2014).
6
[7] P. Walters, An Introduction to Ergodic Theory, Springer Verlag, 1982.
7