2018
6
1
0
0
$mathcal{N}$Fuzzy UPAlgebras and its level subsets
2
2
In this paper, $mathcal{N}$fuzzy UPsubalgebras (resp., $mathcal{N}$fuzzy UPfilters, $mathcal{N}$fuzzy UPideals and $mathcal{N}$fuzzy strongly UPideals) of UPalgebras are introduced and proved its generalizations and characteristic $mathcal{N}$fuzzy sets of UPsubalgebras (resp., UPfilters, UPideals and strongly UPideals).Further, we discuss the relations between $mathcal{N}$fuzzy UPsubalgebras (resp., $mathcal{N}$fuzzy UPfilters, $mathcal{N}$fuzzy UPideals and $mathcal{N}$fuzzy strongly UPideals) and its level subsets.
1

1
24


M.
Songsaeng
University of Phayao, Phayao, Thailan
University of Phayao, Phayao, Thailan
Thailand
metawee.faith@gmail.com


A.
Iampan
University of Phayao, Phayao, Thailand
University of Phayao, Phayao, Thailand
Thailand
aiyared.ia@up.ac.th
UPalgebra
$mathcal{N}$fuzzy UPsubalgebra
$mathcal{N}$fuzzy UPfilter
$mathcal{N}$fuzzy UPideal
$mathcal{N}$fuzzy strongly UPideal
A note on the extended total graph of commutative rings
2
2
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 amultiplicativeprime 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.
1

25
33


F.
Esmaeili Khalil Saraei
University of Tehran
University of Tehran
Iran
f.esmaeili.kh@ut.ac.ir


E.
Navidinia
Department of Mathematics, University of Guilan, Rasht, Iran
Department of Mathematics, University of
Iran
elnaz.navidinia@yahoo.com
Total graph
prime ideal
multiplicativeprime subset
Nonreduced rings of small order and their maximal graph
2
2
Let $R$ be a commutative ring with nonzero identity. Let $Gamma(R)$ denotes the maximal graph corresponding to the nonunit elements of R, that is, $Gamma(R)$is a graph with vertices the nonunit 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 nonreduced ring $R$ with $n$ nonunits? For $n leq 100$, a complete list of nonreduced decomposable rings $R = prod_{i=1}^{k}R_i$ (up to cardinalities of constituent local rings $R_i$'s) with n nonunits 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
1

35
44


A.
Sharma
Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India
Department of Mathematics, Faculty of Mathematical
India
anjanaarti@gmail.com


A.
Gaur
Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India
Department of Mathematics, Faculty of Mathematical
India
agaur@maths.du.ac.in
Nonreduced ring
Jacobson radical
maximal graphs
center
median
Tight Closure of a Graded Ideal Relative to a Graded Module
2
2
In this paper we will study the tight closure of a graded ideal relative to a graded Module.
1

45
54


F.
Dorostkar
Department of Mathematics, University of Guilan, Rasht, Iran
Department of Mathematics, University of
Iran
dorostkar@guilan.ac.ir


R.
Khosravi
Department of Mathematics, University of Guilan, Rasht, Iran
Department of Mathematics, University of
Iran
khosravi@phd.guilan.ac.ir
graded ring
graded ideal
graded module
tight closure relative to a module
tightly closed relative to a module
Essential subhypermodules and their properties
2
2
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.
1

55
66


B.
Talaee
Department of Mathematics, Faculty of Basic Sciences, Babol Noshirvani University of Technology, Babol, Iran.
Department of Mathematics, Faculty of Basic
Iran
behnamtalaee@nit.ac.ir
Hyperring
Hypermodule
Hssential subhypermodule
Hssential monomorphism
Identities in $3$prime nearrings with left multipliers
2
2
Let $mathcal{N}$ be a $3$prime nearring 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 nearring$mathcal{N}$ 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 $x, yinmathcal{N}$.
1

67
77


M.
Ashraf
Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India
Department of Mathematics, Faculty of Science,
India
mashraf80@hotmail.com


A.
Boua
Department of Mathematics, Physics and Computer Science, Sidi Mohammed Ben Abdellah University,Taza, Morocco
Department of Mathematics, Physics and Computer
Morocco
abdelkarimboua@yahoo.fr
$3$Prime nearring
derivations
commutativity
left multiplier