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Bijan Davvaz
Yazd University
Mathematics

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 1 
Star Projective and Star Injective Hv-Modules Mortazavi, A.; Davvaz, Bijan
Journal of the Indonesian Mathematical Society Volume 24 Number 1 (April 2018)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.24.1.490.79-94

Abstract

In this paper, we introduce the concepts of product and directsum, star projective and star injective in $H_v$-modules. Weinvestigate generalizations of some notions in homological algebrato prove the five lemma and star projective and star injectivetheorems in $H_v$-modules. We determine  equivalent conditions for split sequences in $H_v$-modules and  present some related results.
FOUNDATIONS OF ORDERED (SEMI)HYPERRINGS Davvaz, Bijan; Omidi, S.
Journal of the Indonesian Mathematical Society Volume 22 Number 2 (October 2016)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.22.2.233.131-150

Abstract

In this paper, we introduce the notion of general hyperring $(R,+,\cdot)$ besides a binary relation $\le $, where $\le $ is a partial order such that satisfies the conditions: (1) If $a \le b$, then $a+c \le b+c$, meaning that for any $x \in a+c$, there exists $y \in b+c$ such that $x\le y$. The case $c+a\le c+b$ is defined similarly. (2) If $a \le b$ and $c \in R$, then $a\cdot c \le b\cdot c$, meaning that for any $x\in a\cdot c$, there exists $y\in b\cdot c$ such that $x\le y$. The case $c\cdot a \le c\cdot b$ is defined similarly. This structure is called an ordered general hyperring. Also, we present several examples of ordered general hyperrings and prove some results in this respect. By using the notion of pseudoorder on an ordered general hyperring $(R,+,\cdot,\le)$, we obtain an ordered ring. Moreover, we study some properties of pseudoorder on an ordered general hyperring.DOI : http://dx.doi.org/10.22342/jims.22.2.233.131-150
ON $(ALPHA ,BETA)$-FUZZY IDEALS OF TERNARY SEMIGROUPS Davvaz, Bijan
Journal of the Indonesian Mathematical Society Volume 19 Number 2 (October 2013)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.19.2.120.123-138

Abstract

In this paper, we introduce the concept of generalizedfuzzy ideals in ternary semigroups, which is a generalization of the fuzzyideals of semigroups. In this regard, we define ($\alpha ,\beta $)-fuzzyleft (right, lateral) ideals, ($\alpha ,\beta $)-fuzzy quasi-ideals and ($\alpha ,\beta $)-fuzzy bi-ideals and invetigate some related properties ofternary semigroups. Special concentration is paid to ($\in ,\in \vee q$)-fuzzy left (right, lateral) ideals, ($\in ,\in \vee q$)-fuzzy quasi-idealsand ($\in ,\in \vee q$)-fuzzy bi-ideals. Finally, wecharacterize regular ternary semigroups in terms of these notions.DOI : http://dx.doi.org/10.22342/jims.19.2.120.123-138
STRONGLY CLEAN ELEMENTS IN A CERTAIN BLOCK MATRIX RING Nikkhah, Abolfazl; Davvaz, Bijan
Journal of the Indonesian Mathematical Society Volume 22 Number 2 (October 2016)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.22.2.259.151-156

Abstract

In this paper, we investigate the concepts of strongly clean, strongly $\pi$-regular and strongly $J_n$-clean related to the ring $A=\begin{pmatrix}R_RM_S\\0S\end{pmatrix}$. Moreover, we give several equivalent conditions such that an element $\alpha\in End(A)$  is strongly clean.DOI : http://dx.doi.org/10.22342/jims.22.2.259.151-156
A SHORT NOTE ON BANDS OF GROUPS Davvaz, Bijan
Journal of the Indonesian Mathematical Society Volume 21 Number 1 (April 2015)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.21.1.151.19-23

Abstract

In this paper we give necessary and sufficient  conditions on a semigroup S that it be semilattice of groups, a normal band  of groups, and a matrix of groups.DOI : http://dx.doi.org/10.22342/jims.21.1.151.19-23
Study of Properties of Several Kinds of Hyperideals in Ordered Ternary Semihypergroups Changphas, Thawhat; Davvaz, Bijan
Journal of the Indonesian Mathematical Society VOLUME 27 NUMBER 2 (July 2021)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.27.2.965.228-239

Abstract

A non-empty subset S together with an associative function f from S × S×S into the family of all non-empty subsets of S is called a ternary semihypergroup. In this paper, we consider a semihypergroup (S, f) besides a binary relation ≤, where ≤ is a partial order relation on S such that satisfies the monotone condition. This structure is called an ordered ternary semihypergroup. We introduce and investigate the notions of bi-hyperideal and quasi-hyperideal in ordered ternary semihyperroups. In particular, we prove that an ordered ternary semihypergroup is left and right simple if and only if it does not contain proper bi-hyperideals
Co-Authors Changphas, Thawhat Mortazavi, A. Nikkhah, Abolfazl Omidi, S.