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ELEMENTARY TOPICS ON WEAK POLYGROUPS
Davvaz, B. Korean Mathematical Society 2003 대한수학회보 Vol.40 No.1
In this paper, we further develop the weak polygroup theory, we define quotient weak polygroup and then the fundamental homomorphism theorem of group theory is derived in the context of weak polygroups. Also, we consider the fundamental relation $\beta$$^{*}$ defined on a weak polygroup and define a functor from the category of all weak polygroups into the category of all fundamental groups.s.
STRONG REGULARITY AND FUZZY STRONG REGULARITY IN SEMIHYPERGROUPS
Davvaz, B. 한국전산응용수학회 2000 Journal of applied mathematics & informatics Vol.7 No.1
In this paper we introduce the concept of a fuzzy strongly regular relation on a sumihypergroup, and prove a few results concerning this concept.
INTERVAL-VALUED FUZZY SUBHYPERGROUPS
DAVVAZ, B. 한국전산응용수학회 1999 Journal of applied mathematics & informatics Vol.6 No.1
In this paper we introduce the concept of an interval-valued fuzzy subhypergroup of a hypergroup which is an extended notion of a fuzzy subhypergroup of a hypergroup and give some properties of such subhypergroups.
Davvaz, B. 한국전산응용수학회 2003 Journal of applied mathematics & informatics Vol.11 No.1
The purpose of this paper is to present certain results arising from product between fuzzy $H_{v}$-submodules. In particular, we consider the fundamental relation $\varepsilon$* defined on an $H_{v}$-module and give a property of the fundamental relations and fundamental modules with respect to the fuzzy product of $H_{v}$-modules.
Davvaz, B. Korean Mathematical Society 1999 대한수학회보 Vol.36 No.3
$H_v$-rings first were introduced by Vougiouklis in 1990. Then Darafsheh and the present author defined the $H_v$-ring of fractions $S_{-1}R$ of a commutative hyperring. The largest class of multivalued systems satisfying the module-like axioms is the Hv-module. In this paper we define $H_v$-module of fractions of a hypermodule. Some interesting results concerning this $H_v$-module is proved.
A GENERALIZATION OF HOMOLOGICAL ALGEBRA
Davvaz, B.,Shabani-Solt, H. Korean Mathematical Society 2002 대한수학회지 Vol.39 No.6
Our aim in this paper is to introduce a generalization of some notions in homological algebra. We define the concepts of chain U-complex, U-homology, chain (U, U')-map, chain (U, U')-homotopy and $\mu$-functor. We also obtain some interesting results. We use these results to find a generalization of Lambek Lemma, Snake Lemma, Connecting Homomorphism and Exact Triangle.
ON POLYGROUP HYPERRINGS AND REPRESENTATIONS OF POLYGROUPS
Davvaz, B.,Poursalavati, N.S. Korean Mathematical Society 1999 대한수학회지 Vol.36 No.6
In this paper we introduce matrix representations of polygroups over hyperrings and show such representations induce representations of the fundamental group over the corresponding fundamental ring. We also introduce the notion of a polygroup hyperring generalizing the notion of a group ring. We establish homo-morphisms among various polygroup hyperrings.
ERRATUM TO 'A SHORT NOTE ON QUASI-EXACT SEQUENCES'
Davvaz B. Korean Mathematical Society 2006 대한수학회보 Vol.43 No.1
In this note a modification of Proposition 3.10 of [1] is given.
PRODUCT OF FUZZY ${H_v}-IDEALS$ IN ${H_v}-RINGS$
Davvaz, B. 한국전산응용수학회 2001 The Korean journal of computational & applied math Vol.8 No.3
In this paper we define product between fuzzy ${H_v}-ideals$ of given ${H_v}-rings$. we consider the fundamental relation ${\gamma}^*$ defined on and ${H_v}-ring$ and give some properties of the fundamental relations and fundamental rings with respect to the product of fuzzy ${H_v}-ideals$.
ON $H_v$-SUBGROUPS AND ANTI FUZZY $H_v$-SUBGROUPS
Davvaz, B. 한국전산응용수학회 1998 Journal of applied mathematics & informatics Vol.5 No.1
In this paper we define the concept of anti fuzzy $H_v$-subgroup of an $H_v$ -group and prove a few theorems concerning this concept. We also obtain a necessary and sufficient condition for a fuzzy subset of an $H_v$-group to be an anti fuzzy $H_v$ -subgroup. We also abtain a relation between the fuzzy $H_v$-subgroups and the and the anti fuzzy $H_v$-subgroup.