University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
6
1
2018
06
01
$mathcal{N}$-Fuzzy UP-Algebras and its level subsets
1
24
EN
M.
Songsaeng
University of Phayao, Phayao, Thailan
metawee.faith@gmail.com
A.
Iampan
0000-0002-0475-3320
University of Phayao, Phayao, Thailand
aiyared.ia@up.ac.th
10.22124/jart.2018.10280.1102
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.
UP-algebra,$mathcal{N}$-fuzzy UP-subalgebra,$mathcal{N}$-fuzzy UP-filter,$mathcal{N}$-fuzzy UP-ideal,$mathcal{N}$-fuzzy strongly UP-ideal
https://jart.guilan.ac.ir/article_3023.html
https://jart.guilan.ac.ir/article_3023_d550f339655e87cdab5f6b1b9915fa45.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
6
1
2018
06
01
A note on the extended total graph of commutative rings
25
33
EN
F.
Esmaeili Khalil Saraei
University of Tehran
f.esmaeili.kh@ut.ac.ir
E.
Navidinia
Department of Mathematics, University of Guilan, Rasht, Iran
elnaz.navidinia@yahoo.com
10.22124/jart.2018.10241.1101
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 $p,qin R$, the vertices $p$ and $q$ are adjacent if and only if $rp+sqin H$ for some $r,sin Rsetminus H$. We also study the two (induced) subgraphs $ET_{H}(H)$ and $ET_{H}(Rsetminus H)$, with vertices $H$ and $Rsetminus H$, respectively. Among other things, the diameter and the girth of $ET_{H}(R)$ are also studied.
Total graph,prime ideal,multiplicative-prime subset
https://jart.guilan.ac.ir/article_3024.html
https://jart.guilan.ac.ir/article_3024_b309fd14ca084de2d0ddce47f5d91c50.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
6
1
2018
06
01
Non-reduced rings of small order and their maximal graph
35
44
EN
A.
Sharma
Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India
anjanaarti@gmail.com
A.
Gaur
Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India
agaur@maths.du.ac.in
10.22124/jart.2018.10130.1097
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 $n$, $(1leq n leq 7500)$, $|Center(Gamma(R))|$ attains the bounds in the inequality $1leq |Center(Gamma(R))|leq n$ and for which $n$, $(2leq nleq 100)$, $|Center(Gamma(R))|$ attains the value between the bounds
Non-reduced ring,Jacobson radical,maximal graphs,center,median
https://jart.guilan.ac.ir/article_3025.html
https://jart.guilan.ac.ir/article_3025_8bced734856b35561fe82af4e15d0d5c.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
6
1
2018
06
01
Tight Closure of a Graded Ideal Relative to a Graded Module
45
54
EN
F.
Dorostkar
Department of Mathematics, University of Guilan, Rasht, Iran
dorostkar@guilan.ac.ir
R.
Khosravi
Department of Mathematics, University of Guilan, Rasht, Iran
khosravi@phd.guilan.ac.ir
10.22124/jart.2018.9589.1092
In this paper we will study the tight closure of a graded ideal relative to a graded Module.
graded ring,graded ideal,graded module,tight closure relative to a module,tightly closed relative to a module
https://jart.guilan.ac.ir/article_3026.html
https://jart.guilan.ac.ir/article_3026_973dde807f559bbed7b5db557b368b10.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
6
1
2018
06
01
Essential subhypermodules and their properties
55
66
EN
B.
Talaee
Department of Mathematics, Faculty of Basic Sciences, Babol Noshirvani University of Technology, Babol, Iran.
behnamtalaee@nit.ac.ir
10.22124/jart.2018.9573.1089
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.
Hyperring,Hypermodule,Hssential subhypermodule,Hssential monomorphism
https://jart.guilan.ac.ir/article_3027.html
https://jart.guilan.ac.ir/article_3027_30f9c6ce2a292f8d2cb2a3761cca97f0.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
6
1
2018
06
01
Identities in $3$-prime near-rings with left multipliers
67
77
EN
M.
Ashraf
Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India
mashraf80@hotmail.com
A.
Boua
Department of Mathematics, Physics and Computer Science, Sidi Mohammed Ben Abdellah University,Taza, Morocco
abdelkarimboua@yahoo.fr
10.22124/jart.2018.10093.1096
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: $(i):mathcal{F}^{n}([x, y])in Z(mathcal{N})$, $(ii):mathcal{F}^{n}(xcirc y)in Z(mathcal{N})$,$(iii):mathcal{F}^{n}([x, y])pm(xcirc y)in Z(mathcal{N})$ and $(iv):mathcal{F}^{n}([x, y])pm xcirc yin Z(mathcal{N})$, for all $x, yinmathcal{N}$.
$3$-Prime near-ring,derivations,commutativity,left multiplier
https://jart.guilan.ac.ir/article_3080.html
https://jart.guilan.ac.ir/article_3080_f22f660269f5b24d171ddd9ac1a0c68b.pdf