eng
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2018-06-01
6
1
1
24
10.22124/jart.2018.10280.1102
3023
مقاله پژوهشی
$mathcal{N}$-Fuzzy UP-Algebras and its level subsets
M. Songsaeng
metawee.faith@gmail.com
1
A. Iampan
aiyared.ia@up.ac.th
2
University of Phayao, Phayao, Thailan
University of Phayao, Phayao, Thailand
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.
https://jart.guilan.ac.ir/article_3023_d550f339655e87cdab5f6b1b9915fa45.pdf
UP-algebra
$mathcal{N}$-fuzzy UP-subalgebra
$mathcal{N}$-fuzzy UP-filter
$mathcal{N}$-fuzzy UP-ideal
$mathcal{N}$-fuzzy strongly UP-ideal
eng
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2018-06-01
6
1
25
33
10.22124/jart.2018.10241.1101
3024
مقاله پژوهشی
A note on the extended total graph of commutative rings
F. Esmaeili Khalil Saraei
f.esmaeili.kh@ut.ac.ir
1
E. Navidinia
elnaz.navidinia@yahoo.com
2
University of Tehran
Department of Mathematics, University of Guilan, Rasht, Iran
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.
https://jart.guilan.ac.ir/article_3024_b309fd14ca084de2d0ddce47f5d91c50.pdf
Total graph
prime ideal
multiplicative-prime subset
eng
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2018-06-01
6
1
35
44
10.22124/jart.2018.10130.1097
3025
مقاله پژوهشی
Non-reduced rings of small order and their maximal graph
A. Sharma
anjanaarti@gmail.com
1
A. Gaur
agaur@maths.du.ac.in
2
Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India
Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India
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
https://jart.guilan.ac.ir/article_3025_8bced734856b35561fe82af4e15d0d5c.pdf
Non-reduced ring
Jacobson radical
maximal graphs
center
median
eng
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2018-06-01
6
1
45
54
10.22124/jart.2018.9589.1092
3026
مقاله پژوهشی
Tight Closure of a Graded Ideal Relative to a Graded Module
F. Dorostkar
dorostkar@guilan.ac.ir
1
R. Khosravi
khosravi@phd.guilan.ac.ir
2
Department of Mathematics, University of Guilan, Rasht, Iran
Department of Mathematics, University of Guilan, Rasht, Iran
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
graded ring
graded ideal
graded module
tight closure relative to a module
tightly closed relative to a module
eng
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2018-06-01
6
1
55
66
10.22124/jart.2018.9573.1089
3027
مقاله پژوهشی
Essential subhypermodules and their properties
B. Talaee
behnamtalaee@nit.ac.ir
1
Department of Mathematics, Faculty of Basic Sciences, Babol Noshirvani University of Technology, Babol, Iran.
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
Hyperring
Hypermodule
Hssential subhypermodule
Hssential monomorphism
eng
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
2018-06-01
6
1
67
77
10.22124/jart.2018.10093.1096
3080
مقاله پژوهشی
Identities in $3$-prime near-rings with left multipliers
M. Ashraf
mashraf80@hotmail.com
1
A. Boua
abdelkarimboua@yahoo.fr
2
Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India
Department of Mathematics, Physics and Computer Science, Sidi Mohammed Ben Abdellah University,Taza, Morocco
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 $x, yinmathcal{N}$.
https://jart.guilan.ac.ir/article_3080_f22f660269f5b24d171ddd9ac1a0c68b.pdf
$3$-Prime near-ring
derivations
commutativity
left multiplier