@Article{Songsaeng2018,
author="Songsaeng, M.
and Iampan, A.",
title="$\mathcal{N}$-Fuzzy UP-Algebras and its level subsets",
journal="Journal of Algebra and Related Topics",
year="2018",
volume="6",
number="1",
pages="1-24",
abstract="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.",
issn="2345-3931",
doi="10.22124/jart.2018.10280.1102",
url="https://jart.guilan.ac.ir/article_3023.html"
}
@Article{EsmaeiliKhalilSaraei2018,
author="Esmaeili Khalil Saraei, F.
and Navidinia, E.",
title="A note on the extended total graph of commutative rings",
journal="Journal of Algebra and Related Topics",
year="2018",
volume="6",
number="1",
pages="25-33",
abstract="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.",
issn="2345-3931",
doi="10.22124/jart.2018.10241.1101",
url="https://jart.guilan.ac.ir/article_3024.html"
}
@Article{Sharma2018,
author="Sharma, A.
and Gaur, A.",
title="Non-reduced rings of small order and their maximal graph",
journal="Journal of Algebra and Related Topics",
year="2018",
volume="6",
number="1",
pages="35-44",
abstract="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",
issn="2345-3931",
doi="10.22124/jart.2018.10130.1097",
url="https://jart.guilan.ac.ir/article_3025.html"
}
@Article{Dorostkar2018,
author="Dorostkar, F.
and Khosravi, R.",
title="Tight Closure of a Graded Ideal Relative to a Graded Module",
journal="Journal of Algebra and Related Topics",
year="2018",
volume="6",
number="1",
pages="45-54",
abstract="In this paper we will study the tight closure of a graded ideal relative to a graded Module.",
issn="2345-3931",
doi="10.22124/jart.2018.9589.1092",
url="https://jart.guilan.ac.ir/article_3026.html"
}
@Article{Talaee2018,
author="Talaee, B.",
title="Essential subhypermodules and their properties",
journal="Journal of Algebra and Related Topics",
year="2018",
volume="6",
number="1",
pages="55-66",
abstract="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.",
issn="2345-3931",
doi="10.22124/jart.2018.9573.1089",
url="https://jart.guilan.ac.ir/article_3027.html"
}
@Article{Ashraf2018,
author="Ashraf, M.
and Boua, A.",
title="Identities in $3$-prime near-rings with left multipliers",
journal="Journal of Algebra and Related Topics",
year="2018",
volume="6",
number="1",
pages="67-77",
abstract="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 $x, y\in\mathcal{N}$.",
issn="2345-3931",
doi="10.22124/jart.2018.10093.1096",
url="https://jart.guilan.ac.ir/article_3080.html"
}