$\mathcal{N}$-Fuzzy UP-Algebras and its level subsets
M.
Songsaeng
University of Phayao, Phayao, Thailan
author
A.
Iampan
University of Phayao, Phayao, Thailand
author
text
article
2018
eng
In this paper, $\mathcal{N}$-fuzzy UP-subalgebras (resp., $\mathcal{N}$-fuzzy UP-filters, $\mathcal{N}$-fuzzy UP-ideals and $\mathcal{N}$-fuzzy strongly UP-ideals) of UP-algebras are introduced and proved its generalizations and characteristic $\mathcal{N}$-fuzzy sets of UP-subalgebras (resp., UP-filters, UP-ideals and strongly UP-ideals).Further, we discuss the relations between $\mathcal{N}$-fuzzy UP-subalgebras (resp., $\mathcal{N}$-fuzzy UP-filters, $\mathcal{N}$-fuzzy UP-ideals and $\mathcal{N}$-fuzzy strongly UP-ideals) and its level subsets.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
6
v.
1
no.
2018
1
24
https://jart.guilan.ac.ir/article_3023_d550f339655e87cdab5f6b1b9915fa45.pdf
dx.doi.org/10.22124/jart.2018.10280.1102
A note on the extended total graph of commutative rings
F.
Esmaeili Khalil Saraei
University of Tehran
author
E.
Navidinia
Department of Mathematics, University of Guilan, Rasht, Iran
author
text
article
2018
eng
Let $R$ be a commutative ring and $H$ a nonempty proper subset of $R$.In this paper, the extended total graph, denoted by $ET_{H}(R)$ is presented, where $H$ is amultiplicative-prime subset of $R$. It is the graph with all elements of $R$ as vertices, and for distinct $p,q\in R$, the vertices $p$ and $q$ are adjacent if and only if $rp+sq\in H$ for some $r,s\in R\setminus H$. We also study the two (induced) subgraphs $ET_{H}(H)$ and $ET_{H}(R\setminus H)$, with vertices $H$ and $R\setminus H$, respectively. Among other things, the diameter and the girth of $ET_{H}(R)$ are also studied.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
6
v.
1
no.
2018
25
33
https://jart.guilan.ac.ir/article_3024_b309fd14ca084de2d0ddce47f5d91c50.pdf
dx.doi.org/10.22124/jart.2018.10241.1101
Non-reduced rings of small order and their maximal graph
A.
Sharma
Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India
author
A.
Gaur
Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India
author
text
article
2018
eng
Let $R$ be a commutative ring with nonzero identity. Let $\Gamma(R)$ denotes the maximal graph corresponding to the non-unit elements of R, that is, $\Gamma(R)$is a graph with vertices the non-unit elements of $R$, where two distinctvertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $R$containing both. In this paper, we investigate that for a given positive integer $n$, is there a non-reduced ring $R$ with $n$ non-units? For $n \leq 100$, a complete list of non-reduced decomposable rings $R = \prod_{i=1}^{k}R_i$ (up to cardinalities of constituent local rings $R_i$'s) with n non-units is given. We also show that for which $n$, $(1\leq n \leq 7500)$, $|Center(\Gamma(R))|$ attains the bounds in the inequality $1\leq |Center(\Gamma(R))|\leq n$ and for which $n$, $(2\leq n\leq 100)$, $|Center(\Gamma(R))|$ attains the value between the bounds
Journal of Algebra and Related Topics
University of Guilan
2345-3931
6
v.
1
no.
2018
35
44
https://jart.guilan.ac.ir/article_3025_8bced734856b35561fe82af4e15d0d5c.pdf
dx.doi.org/10.22124/jart.2018.10130.1097
Tight Closure of a Graded Ideal Relative to a Graded Module
F.
Dorostkar
Department of Mathematics, University of Guilan, Rasht, Iran
author
R.
Khosravi
Department of Mathematics, University of Guilan, Rasht, Iran
author
text
article
2018
eng
In this paper we will study the tight closure of a graded ideal relative to a graded Module.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
6
v.
1
no.
2018
45
54
https://jart.guilan.ac.ir/article_3026_973dde807f559bbed7b5db557b368b10.pdf
dx.doi.org/10.22124/jart.2018.9589.1092
Essential subhypermodules and their properties
B.
Talaee
Department of Mathematics, Faculty of Basic Sciences, Babol Noshirvani University of Technology, Babol, Iran.
author
text
article
2018
eng
Let R be a hyperring (in the sense of [8]) andM be a hypermodule on R. In this paper we will introduce and study a class of subhypermodules of M. We will study on intersection of this kind of subhypermodules a give some suitable results about them. We will proceed to give some in- teresting results about the complements, direct sums and independency of this kind of subhypermodules.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
6
v.
1
no.
2018
55
66
https://jart.guilan.ac.ir/article_3027_30f9c6ce2a292f8d2cb2a3761cca97f0.pdf
dx.doi.org/10.22124/jart.2018.9573.1089
Identities in $3$-prime near-rings with left multipliers
M.
Ashraf
Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India
author
A.
Boua
Department of Mathematics, Physics and Computer Science, Sidi Mohammed Ben Abdellah University,Taza, Morocco
author
text
article
2018
eng
Let $\mathcal{N}$ be a $3$-prime near-ring with the center$Z(\mathcal{N})$ and $n \geq 1$ be a fixed positive integer. Inthe present paper it is shown that a $3$-prime near-ring$\mathcal{N}$ is a commutative ring if and only if it admits aleft multiplier $\mathcal{F}$ satisfying any one of the followingproperties: $(i)\:\mathcal{F}^{n}([x, y])\in Z(\mathcal{N})$, $(ii)\:\mathcal{F}^{n}(x\circ y)\in Z(\mathcal{N})$,$(iii)\:\mathcal{F}^{n}([x, y])\pm(x\circ y)\in Z(\mathcal{N})$ and $(iv)\:\mathcal{F}^{n}([x, y])\pm x\circ y\in Z(\mathcal{N})$, for all $x, y\in\mathcal{N}$.
Journal of Algebra and Related Topics
University of Guilan
2345-3931
6
v.
1
no.
2018
67
77
https://jart.guilan.ac.ir/article_3080_f22f660269f5b24d171ddd9ac1a0c68b.pdf
dx.doi.org/10.22124/jart.2018.10093.1096