University of Guilan Journal of Algebra and Related Topics 2345-3931 6 1 2018 06 01 $\mathcal{N}$-Fuzzy UP-Algebras and its level subsets 1 24 3023 10.22124/jart.2018.10280.1102 EN M. Songsaeng University of Phayao, Phayao, Thailan A. Iampan University of Phayao, Phayao, Thailand Journal Article 2018 04 30 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 considered their 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.

https://jart.guilan.ac.ir/article_3023_eb6a1cfb82810f057804c9773be257d9.pdf

University of Guilan Journal of Algebra and Related Topics 2345-3931 6 1 2018 06 01 A note on the extended total graph of commutative rings 25 33 3024 10.22124/jart.2018.10241.1101 EN F. Esmaeili Khalil Saraei University of Tehran E. Navidinia Department of Mathematics, University of Guilan, Rasht, Iran Journal Article 2018 04 25 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 a multiplicative-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.

https://jart.guilan.ac.ir/article_3024_c7a72ce759419a2bcd9ddd57dcf4da67.pdf

University of Guilan Journal of Algebra and Related Topics 2345-3931 6 1 2018 06 01 Non-reduced rings of small order and their maximal graph 35 44 3025 10.22124/jart.2018.10130.1097 EN A. Sharma Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India A. Gaur Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India Journal Article 2018 04 17 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 distinct vertices $a$ 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

https://jart.guilan.ac.ir/article_3025_8bced734856b35561fe82af4e15d0d5c.pdf

University of Guilan Journal of Algebra and Related Topics 2345-3931 6 1 2018 06 01 Tight Closure of a Graded Ideal Relative to a Graded Module 45 54 3026 10.22124/jart.2018.9589.1092 EN F. Dorostkar Department of Mathematics, University of Guilan, Rasht, Iran R. Khosravi Department of Mathematics, University of Guilan, Rasht, Iran Journal Article 2018 02 13 In this paper we will study the tight closure of a graded ideal relative to a graded Module.

https://jart.guilan.ac.ir/article_3026_973dde807f559bbed7b5db557b368b10.pdf

University of Guilan Journal of Algebra and Related Topics 2345-3931 6 1 2018 06 01 Essential subhypermodules and their properties 55 66 3027 10.22124/jart.2018.9573.1089 EN B. Talaee Department of Mathematics, Faculty of Basic Sciences, Babol Noshirvani University of Technology, Babol, Iran. Journal Article 2018 01 20 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.

https://jart.guilan.ac.ir/article_3027_30f9c6ce2a292f8d2cb2a3761cca97f0.pdf

University of Guilan Journal of Algebra and Related Topics 2345-3931 6 1 2018 06 01 Identities in $3$-prime near-rings with left multipliers 67 77 3080 10.22124/jart.2018.10093.1096 EN M. Ashraf Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India A. Boua Department of Mathematics, Physics and Computer Science, Sidi Mohammed Ben Abdellah University,Taza, Morocco Journal Article 2018 04 09 Let $\mathcal{N}$ be a $3$-prime near-ring with the center $Z(\mathcal{N})$ and $n \geq 1$ be a fixed positive integer. In the present paper it is shown that a $3$-prime near-ring $\mathcal{N}$ is a commutative ring if and only if it admits a left multiplier $\mathcal{F}$ satisfying any one of the following properties: $(i)\:\mathcal{F}^{n}([x, y])\in Z(\mathcal{N})$, $(ii)\:\mathcal{F}^{n}(x\circ y)\in Z(\mathcal{N})$, $(iii)\:\mathcal{F}^{n}([x, y])\pm(x\circ y)\in Z(\mathcal{N})$ and $(iv)\:\mathcal{F}^{n}([x, y])\pm x\circ y\in Z(\mathcal{N})$, for all $x, y\in\mathcal{N}$.

https://jart.guilan.ac.ir/article_3080_2bfb17a33939beaf9b8352a63a5aa703.pdf