2016
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HXhypergroups associated with the direct products of some ${bf Z}/n {bf Z}$
2
2
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.
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1
15


Piergiulio
Corsini
University of Udine
University of Udine
Italy
$HX$group
Fuzzy grade
[[1] R. Ameri, M.M. Zahedi, Hypergroup and join space induced by a fuzzy subset, PU.M.A., (1997) vol. 8,##[2] P. Cosini, On Chinese hyperstructures, J. Discrete Math. Sci and Cryptography, Vol 6 (2003), no 23,##[3] P. Corsini, Join Spaces, Power Sets, Fuzzy Sets, Proc. Fifth International Congress on A.H.A., 1993, Iasi,##[4] P. Corsini, A new connection between hypergroups and fuzzy sets, Southeast Bulletin of Math., 27 (2003)##[5] P. Corsini, Hyperstructures associated with ordered sets, Bull. the Greek Math. Soc., vol. 48, (2003) 718.##[6] P. Corsini, Join Spaces, multivalued functions and soft sets, Proc. Int. Conf. Alg. 2010, (ICA 2010),##Universitas Gadjah Mada and the Southeast Asian Math.##[7] P. Corsini, HXgroups and Hypergroup, Analele Univ. "Ovidius", Math. Series n. 3, (2016).##[8] P. Corsini, Hypergroups associated with HX groups, accepted by Analele Univ. "Ovidius", 2016.##[9] P. Corsini, Prolegomena of Hypergroup Theory, Aviani Editore, (1993).##[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.##4, (2003) 275288.##[11] P. Corsini, I. Cristea, Fuzzy grade of i.p.s. hypergroups of order 7, Iran J. of Fuzzy Systems, 1 (2004)##[12] P. Corsini, I. Cristea, Fuzzy sets and non complete 1hypergroups, An. St. Univ. Ovidius Constanta, 13##(1) (2005) 2754.##[13] P. Corsini and B. Davvaz, New connections among multivalued functions, hyperstructures and fuzzy sets,##J. Journal Math. Stat., (JJMS) 3 (3) (2010) 133  150.##[14] P. Corsini and V. LeoreanuFotea, Join Spaces associated with Fuzzy Sets, J. Combin. Inform. Sys. Sci.,##vol. 20, n. 1 (1995) 293303.##[15] P. Corsini, V. Leoreanu, Applications of Hyperstructure Theory, Advances in Mathematics, Kluwer Aca##demic Publishers, (2003).##[16] P. Corsini and V. LeoreanuFotea, On the grade of a sequence of fuzzy sets and join spaces determined##by a hypergraph, Southeast Asian Bull. Math., 34 (2010) 113119.##[17] P. Corsini, V. LeoreanuFotea, A. Iranmanesh, On the sequence of join spaces and membership functions##determined by a hypergraph, J. Mult. Logic Soft Comput., vol. 14, issue 6, (2008) 565577.##[18] P. Corsini, V. LeoreanuFotea, A.M. Lepellere, Fuzzy grade of some hyperstructures, Int. J. Alg. Hyper##struc. Appl., no. 2, Tehran, Iran##[19] P. Corsini and R. Mahjoob, Multivalued functions, fuzzy subsets and join spaces, Ratio Mathematica, 20##(2010) 141.##[20] I. Cristea, A property of the connection between fuzzy sets and hypergroupoids, Italian J. Pure Appl.##Math., 21 (2007) 7382.##[21] B. Davvaz, Hypergroups and fuzzy sets, Proc. 4th Seminar on Fuzzy Sets and it's Applications, University##of Mazandaran, Babolsar, Iran, (2003), 4554.##[22] F. Yuming Algebraic hyperstructures obtained from algebraic structures with binary fuzzy binary relations,##Italian J. Pure Appl. Math., 25 (2009) 49.##[23] S. Hoskova, P. Chvalina, C. Rackova, Noncommutative join spaces of integral operators and related hy##perstructures, Advances MT, 1 (2000) 724.##[24] L. Hongxing, D. Qinzhi and W. Peizhuang, Hypergroup (I). Busefal, Vol. 23, (1985)##[25] L. Hongxing, W. Peizhuang, Hypergroup Busefal, (II), vol. 25, (1986).##[26] L. Hongxing, HXGroups, Busefal, Vol. 33, (1987).##[27] M. Honghai, Uniform HXgroups, Busefal Vol. 47, (1991).##[28] A. Maturo, I. Tofan, Iperstrutture, strutture fuzzy ed applicazioni, monograa di 168 pagine, pubblicazione##nanziata con i fondi del progetto internazionale SocratesErasmus 2000/2001, ItaliaRomania, Dierre##Edizioni San Salvo, agosto.##[29] W. Prenowitz, J. Jantosciak, Join Geometries, SpringerVerlag UTM, (1979).##[30] S. J. Rasovic, Hyperrings constructed by multiendomorphisms of hypergroups, Proceedings of the 10th##International Congress on AHA, Brno, (2008)##[31] K. Seramidis, A. Kehagias, M. Konstantinidou, The Lfuzzy Corsini join hyperoperation, Italian Journal##of Pure and Applied Mathematics, 12 (2003).##[32] S. Spartalis, The hyperoperation relation and the Corsini's partial or not partial hypergroupoid, Italian J.##Pure Appl. Math., 24 (2008) 97{112.##[33] M. Stefanescu, I. Cristea, On the fuzzy grade of hypergroups, Fuzzy Sets and Systems, 159 (2008).##[34] T. Vougiouklis Hyperstructures and their representations, Hadronic Press Inc. (1994).##[35] M. Yavari, Corsini's method and construction of join spaces, Italian J. Pure Appl. Math., 23 (2008)##[36] Z. Zhenliang, The properties of HXGroups, Italian J. Pure Appl. Math., Vol. 2, (1997).##[37] Z. Zhenliang, Classications of HXGroups and their chains of normal subgroups, Italian J. Pure Appl.##Math., Vol. 5, (1999).##[38] Z. Baojie, L. Hongxing, HXtype Chaotic (hyperchaotic) System Based on Fuzzy Inference Modeling,##Italian J. Pure Appl. Math., to appear.##]
A note on the order graph of a group
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2
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 $Hbig{}K$ or $Kbig{}H$. 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.
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17
24


Hamid Reza
Dorbidi
University of Jiroft
University of Jiroft
Iran
hr_dorbidi@yahoo.com
Connected graph
Frobenius group
Order graph
Prime graph
[[1] J. A. Bondi, J. S. Murty, Graph theory with applications, American Elsevier Publishing Co, INC, 1997.##[2] Y. Chen, On Thompson’s conjecture, J. Algebra 15 (1996), 184193.##[3] J. A. Gallian, Contemporary Abstract Algebra, D. C. Heath and company, 1994.##[4] B. Huppert, Character Theory of Finite Groups, De Gruyter Expositions in Mathematics, New York 1998.##[5] Sh. Payrovi, H. Pasebani, The Order Graphs of Groups, J Algebraic Structures and Their Applications, 1##(no 1) ( 2014 ), 110.##[6] J. S. Wiliams, Prime Graph Components of Finite Groups, J. Algebra 69 (1981), 487513.##]
Exact sequences of extended $d$homology
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2
In this article, we show the existence of certain exact sequences with respect to two homology theories, called dhomology and extended dhomology. We present sufficient conditions for the existence of long exact extended d homology sequence. Also we give some illustrative examples.
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25
38


Mohammad Zaher
Kazemi Baneh
University of Kurdistan
University of Kurdistan
Iran
zaherkazemi@uok.ac.ir


Seyed Naser
Hosseini
Shahid Bahonar University of Kerman
Shahid Bahonar University of Kerman
Iran
nhoseini@uk.ac.ir
kernel
image
abelian category
standard homology
(extended) dhomology
exact sequence
[[1] F. Borceux, D. Bourn, MalCev, Protomodular, Homological and SemiAbelian Categories, Kluwer Academic##Publishers, 2004.##[2] S.N. Hosseini, M.Z.Kazemi Baneh, Homology with respect to a Kernel Transformation, Turk. J. Math. 35##(2011), 169186.##[3] M.Z. KazemiBaneh,Homotopic Chain Maps Have Equal sHomology and dHomology, Int. J. Math. Math.##Sci., Volume 2016, 2016.##[4] M.Z. Kazemi Baneh, Homotopic chaim maps have equal extended dHomology, 47th Annual Iranian Mathematics Conference, Kharazmi University, Aug. 2016.##[5] S. MacLane, Categories for the Working Mathematician, 2nd edition, SpringerVerlag, 1998.##[6] M.S. Osborne, Basic Homological Algebra, SpringerVerlag, 2000.##]
The principal ideal subgraph of the annihilatingideal graph of commutative rings
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2
Let $R$ be a commutative ring with identity and $mathbb{A}(R)$ be the set of ideals of $R$ with nonzero annihilators. In this paper, we first introduce and investigate the principal ideal subgraph of the annihilatingideal 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 $mathbb{AG}_s(R)$.
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39
52


Reza
Taheri
Islamic Azad University, Science and Research Branch, Tehran, Iran
Islamic Azad University, Science and Research
Iran


Abolfazl
Tehranian
Islamic Azad University, Science and Research Branch, Tehran, Iran
Islamic Azad University, Science and Research
Iran
tehranian1340@yahoo.com
commutative rings
annihilatingideal
principal ideal
graph
[[1] G. Aalipour, S. Akbari, M. Behboodi, R. Nikandish and M. J. Nikmehr and F. Shahsavari, The classification of the annihilatingideal graph of a commutative ring, Algebra Colloquium 21 (2014) 249256.##[2] G. Aalipour, S. Akbari, R. Nikandish, M. J. Nikmehr and F. Shahsavari, On the coloring of the annihilatingideal graph of a commutative ring, Discrete Math. 312 (2012) 26202626.##[3] G. Aalipour, S. Akbari, R. Nikandish, M. J. Nikmehr and F. Shahsavari, Minimal prime ideals and cycles in##annihilatingideal graphs, Rocky Mountain J. Math. 5 (2013) 14151425.##[4] F. Aliniaeifard and M. Behboodi, Rings whose annihilatingideal graphs have positive genus, J. Algebra Appl. 11, 1250049 (2012) [13 pages] DOI: 10.1142/S0219498811005774.##[5] F. Aliniaeifard, M. Behboodi, E. MehdiNezhad, and A.M. Rahimi, On the diameter and girth of an annihilatingideal graph, to apear.##[6] F. Aliniaeifard, M. Behboodi, E. MehdiNezhad and A. M. Rahimi, The annihilatingideal graph of a commutative ring with respect to an ideal, Commun. Algebra 42 (2014) 22692284.##[7] D. F. Anderson and A. Badawi, The total graph of a commutative ring, J. Algebra 320 (2008) 27062719.##[8] D. F. Anderson and P. S. Livingston, The zerodivisor graph of a commutative ring, J. Algebra 217 (1999) 434447.##[9] L. Anderson, A First Course in Discrete Mathematice, Springer Undergraduate Mathematics Series,2000.##[10] M. Baziar, E. Momtahan and S. Safaeeyan, A zerodivisor graph for modules with respect to their (first) dual, J. Algebra Appl. 12, 1250151 (2013) [11 pages] DOI: 10.1142/S0219498812501514.##[11] M. Behboodi, Zero divisor graphs for modules over commutative rings, J. Commut. Algebra 4 (2012) 175197.##[12] M. Behboodi, Z. Rakeei,The annihilatingideal graph of commutative rings I, J. Algebra Appl. 10 (2011) 727739.##[13] M. Behboodi, Z. Rakeei,The annihilatingideal graph of commutative rings II, J. Algebra Appl. 10 (2011) 740753.##[14] I. Chakrabarty, S. Ghosh, T. K. Mukherjee and M. K. Sen, Intersection graphs of ideals of rings, Discrete Math. 309 (2009), 53815392.##[15] W. K. Nicholson and E. s , anchezCampos, Rings with the dual of the isomorphism theorem , J. Algebra 271 (1) (2004), 391406.##[16] R. Nikandish and H. R. Maimani, Dominating sets of the annihilatingideal graphs, Electronic Notes in Discrete Math. 45 (2014) 1722.##[17] R. Y. Sharp, Steps in commutative algebra Cambridge University Press, Cambridge, 1991.##[18] R. Taheri, M. Behboodi and A. Tehranian, The spectrum subgraph of the annihilatingideal graph of a commutative ring, J. Algebra Appl. 14 (2015) [19 page].##]
The concept of logic entropy on Dposets
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2
In this paper, a new invariant called {it logic entropy} for dynamical systems on a Dposet 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 KolmogorovSinai theorem is given.
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53
61


Uosef
Mohammadi
University of Jiroft
University of Jiroft
Iran
u.mohamadi@ujiroft.ac.ir
Dposet
logic entropy
dynamical system
isomorphism
$ m $generator
[[1] G. Birkhoff, J. Von Neumann, The logic of quantum mechanics, Ann. Math. 37, 823–842 (1936).##[2] M. Ebrahimi, B. Mosapour, The concept of entropy on Dposets, Cankaya University Journal of Science and Engineering, 10, 137–151 (2013).##[3] F. Kopka and F. Chovanec, Dposets, Mathematica Slovaca 44, 21–34 (1994).##[4] T. Kroupa, Conditional probability on MValgebras, Fuzzy Sets and Systems. 369–381 (2005).##[5] U. Mohammadi, Weighted entropy function as an extension of the KolmogorovSinai entropy, U. P. B. Sci. Series A, no. 4, 117–122 (2015).##[6] U. Mohammadi, Relative entropy functional of relative dynamical systems, Cankaya University Journal of Science and Engineering, no. 2, 29–38 (2014).##[7] P. Walters, An Introduction to Ergodic Theory, Springer Verlag, 1982.##]