Volume 10 (2022-2023)
Volume 9 (2021-2022)
Volume 8 (2020-2021)
Volume 7 (2019-2020)
Volume 6 (2018-2019)
Volume 5 (2017-2018)
Volume 4 (2016-2017)
Volume 3 (2015-2016)
Volume 2 (2014-2015)
Volume 1 (2013-2014)
Number of Articles: 7
BAER AND QUASI-BAER PROPERTIES OF SKEW PBW EXTENSIONS
Volume 7, Issue 1 , September 2019, Pages 1-24
Abstract
A ring $R$ with an automorphism $\sigma$ and a $\sigma$-derivation $\delta$ is called $\delta$-quasi-Baer (resp., $\sigma$-invariant quasi-Baer) if the right annihilator of every $\delta$-ideal (resp., $\sigma$-invariant ideal) of $R$ is generated by an idempotent, as a right ideal. In this paper, we ... Read MoreCOTORSION DIMENSIONS OVER GROUP RINGS
Volume 7, Issue 1 , September 2019, Pages 25-32
Abstract
Let $\Gamma$ be a group, $\Gamma'$ a subgroup of $\Gamma$ with finite index and $M$ be a $\Gamma$-module. We show that $M$ is cotorsion if and only if it is cotorsion as a $\Gamma'$-module. Using this result, we prove that the global cotorsion dimensions of rings $Z\Gamma$ and $Z\Gamma'$ are equal. Read MoreHYPERIDEALS IN M-POLYSYMMETRICAL HYPERRINGS
Volume 7, Issue 1 , September 2019, Pages 33-50
Abstract
An M-polysymmetrical hyperring $(R,+,\cdot )$ is an algebraic system, where $(R,+)$ is an M-polysymmetrical hypergroup, $(R,\cdot )$ is a semigroup and $\cdot$ is bilaterally distributive over $+$. In this paper, we introduce the concept of hyperideals of an M-polysymmetrical hyperring and by using this ... Read MoreON THE REFINEMENT OF THE UNIT AND UNITARY CAYLEY GRAPHS OF RINGS
Volume 7, Issue 1 , September 2019, Pages 51-68
Abstract
Let $R$ be a ring (not necessarily commutative) with nonzero identity. We define $\Gamma(R)$ to be the graph with vertex set $R$ in which two distinct vertices $x$ and $y$ are adjacent if and only if there exist unit elements $u,v$ of $R$ such that $x+uyv$ is a unit of $R$. In this paper, basic properties ... Read MoreGENERALIZED UNI-SOFT INTERIOR IDEALS IN ORDERED SEMIGROUPS
Volume 7, Issue 1 , September 2019, Pages 69-82
Abstract
For all M,N∈P(U) such that M⊂N, we first introduced the definitions of (M,N)-uni-soft ideals and (M,N)-uni-soft interior ideals of an ordered semigroup and studied them. When M=∅ and N=U, we meet the ordinary soft ones. Then we proved that in regular and in intra-regular ordered semigroups ... Read MoreNEW METHODS FOR CONSTRUCTING GENERALIZED GROUPS, TOPOLOGICAL GENERALIZED GROUPS, AND TOP SPACES
Volume 7, Issue 1 , September 2019, Pages 83-94
Abstract
The purpose of this paper is to introduce new methods for constructing generalized groups, generalized topological groups and top spaces. We study some properties of these structures and present some relative concrete examples. Moreover, we obtain generalized groups by using of Hilbert spaces ... Read MoreON THE NORMALITY OF t-CAYLEY HYPERGRAPHS OF ABELIAN GROUPS
Volume 7, Issue 1 , September 2019, Pages 95-103