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Bijan Davvaz
Yazd University
Mathematics

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 1 
ON $(ALPHA ,BETA)$-FUZZY IDEALS OF TERNARY SEMIGROUPS Bijan Davvaz
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
A SHORT NOTE ON BANDS OF GROUPS Bijan Davvaz
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
FOUNDATIONS OF ORDERED (SEMI)HYPERRINGS Bijan Davvaz; S. Omidi
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
STRONGLY CLEAN ELEMENTS IN A CERTAIN BLOCK MATRIX RING Abolfazl Nikkhah; Bijan Davvaz
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 $A=\begin{pmatrix}R&_RM_S\\0&S\end{pmatrix}$. 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
Co-Authors Abolfazl Nikkhah S. Omidi