ORIGINAL_ARTICLE
$\mathcal{N}$-Fuzzy UP-Algebras and its level subsets
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
2018-06-01T11:23:20
2018-12-11T11:23:20
1
24
10.22124/jart.2018.10280.1102
UP-algebra
$mathcal{N}$-fuzzy UP-subalgebra
$mathcal{N}$-fuzzy UP-filter
$mathcal{N}$-fuzzy UP-ideal
$mathcal{N}$-fuzzy strongly UP-ideal
M.
Songsaeng
metawee.faith@gmail.com
true
1
University of Phayao, Phayao, Thailan
University of Phayao, Phayao, Thailan
University of Phayao, Phayao, Thailan
AUTHOR
A.
Iampan
aiyared.ia@up.ac.th
true
2
University of Phayao, Phayao, Thailand
University of Phayao, Phayao, Thailand
University of Phayao, Phayao, Thailand
LEAD_AUTHOR
ORIGINAL_ARTICLE
A note on the extended total graph of commutative rings
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.
https://jart.guilan.ac.ir/article_3024_b309fd14ca084de2d0ddce47f5d91c50.pdf
2018-06-01T11:23:20
2018-12-11T11:23:20
25
33
10.22124/jart.2018.10241.1101
Total graph
prime ideal
multiplicative-prime subset
F.
Esmaeili Khalil Saraei
f.esmaeili.kh@ut.ac.ir
true
1
University of Tehran
University of Tehran
University of Tehran
LEAD_AUTHOR
E.
Navidinia
elnaz.navidinia@yahoo.com
true
2
Department of Mathematics, University of Guilan, Rasht, Iran
Department of Mathematics, University of Guilan, Rasht, Iran
Department of Mathematics, University of Guilan, Rasht, Iran
AUTHOR
ORIGINAL_ARTICLE
Non-reduced rings of small order and their maximal graph
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
https://jart.guilan.ac.ir/article_3025_8bced734856b35561fe82af4e15d0d5c.pdf
2018-06-01T11:23:20
2018-12-11T11:23:20
35
44
10.22124/jart.2018.10130.1097
Non-reduced ring
Jacobson radical
maximal graphs
center
median
A.
Sharma
anjanaarti@gmail.com
true
1
Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India
Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India
Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India
LEAD_AUTHOR
A.
Gaur
agaur@maths.du.ac.in
true
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
Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India
AUTHOR
ORIGINAL_ARTICLE
Tight Closure of a Graded Ideal Relative to a Graded Module
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
2018-06-01T11:23:20
2018-12-11T11:23:20
45
54
10.22124/jart.2018.9589.1092
graded ring
graded ideal
graded module
tight closure relative to a module
tightly closed relative to a module
F.
Dorostkar
dorostkar@guilan.ac.ir
true
1
Department of Mathematics, University of Guilan, Rasht, Iran
Department of Mathematics, University of Guilan, Rasht, Iran
Department of Mathematics, University of Guilan, Rasht, Iran
LEAD_AUTHOR
R.
Khosravi
khosravi@phd.guilan.ac.ir
true
2
Department of Mathematics, University of Guilan, Rasht, Iran
Department of Mathematics, University of Guilan, Rasht, Iran
Department of Mathematics, University of Guilan, Rasht, Iran
AUTHOR
ORIGINAL_ARTICLE
Essential subhypermodules and their properties
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
2018-06-01T11:23:20
2018-12-11T11:23:20
55
66
10.22124/jart.2018.9573.1089
Hyperring
Hypermodule
Hssential subhypermodule
Hssential monomorphism
B.
Talaee
behnamtalaee@nit.ac.ir
true
1
Department of Mathematics, Faculty of Basic Sciences, Babol Noshirvani University of Technology, Babol, Iran.
Department of Mathematics, Faculty of Basic Sciences, Babol Noshirvani University of Technology, Babol, Iran.
Department of Mathematics, Faculty of Basic Sciences, Babol Noshirvani University of Technology, Babol, Iran.
LEAD_AUTHOR
ORIGINAL_ARTICLE
Identities in $3$-prime near-rings with left multipliers
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 $x, y\in\mathcal{N}$.
https://jart.guilan.ac.ir/article_3080_f22f660269f5b24d171ddd9ac1a0c68b.pdf
2018-06-01T11:23:20
2018-12-11T11:23:20
67
77
10.22124/jart.2018.10093.1096
$3$-Prime near-ring
derivations
commutativity
left multiplier
M.
Ashraf
mashraf80@hotmail.com
true
1
Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India
Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India
Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India
LEAD_AUTHOR
A.
Boua
abdelkarimboua@yahoo.fr
true
2
Department of Mathematics, Physics and Computer Science, Sidi Mohammed Ben Abdellah University,Taza, Morocco
Department of Mathematics, Physics and Computer Science, Sidi Mohammed Ben Abdellah University,Taza, Morocco
Department of Mathematics, Physics and Computer Science, Sidi Mohammed Ben Abdellah University,Taza, Morocco
AUTHOR