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 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
2018-06-01
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
1
University of Phayao, Phayao, Thailan
AUTHOR
A.
Iampan
aiyared.ia@up.ac.th
2
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_c7a72ce759419a2bcd9ddd57dcf4da67.pdf
2018-06-01
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
1
University of Tehran
LEAD_AUTHOR
E.
Navidinia
elnaz.navidinia@yahoo.com
2
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
2018-06-01
35
44
10.22124/jart.2018.10130.1097
Non-reduced ring
Jacobson radical
maximal graphs
center
median
A.
Sharma
anjanaarti@gmail.com
1
Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India
LEAD_AUTHOR
A.
Gaur
agaur@maths.du.ac.in
2
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
2018-06-01
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
1
Department of Mathematics, University of Guilan, Rasht, Iran
LEAD_AUTHOR
R.
Khosravi
khosravi@phd.guilan.ac.ir
2
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
2018-06-01
55
66
10.22124/jart.2018.9573.1089
Hyperring
Hypermodule
Hssential subhypermodule
Hssential monomorphism
B.
Talaee
behnamtalaee@nit.ac.ir
1
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_2bfb17a33939beaf9b8352a63a5aa703.pdf
2018-06-01
67
77
10.22124/jart.2018.10093.1096
$3$-Prime near-ring
derivations
commutativity
left multiplier
M.
Ashraf
mashraf80@hotmail.com
1
Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India
LEAD_AUTHOR
A.
Boua
abdelkarimboua@yahoo.fr
2
Department of Mathematics, Physics and Computer Science, Sidi Mohammed Ben Abdellah University,Taza, Morocco
AUTHOR