1. BAER AND QUASI-BAER PROPERTIES OF SKEW PBW EXTENSIONS

E. Hashemi; Kh. Khalilnezhad; M. Ghadiri

Volume 7, Issue 1 , Summer and Autumn 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 More

2. COTORSION DIMENSIONS OVER GROUP RINGS

A. Hajizamani

Volume 7, Issue 1 , Summer and Autumn 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 More

3. HYPERIDEALS IN M-POLYSYMMETRICAL HYPERRINGS

M. A. Madani; S. Mirvakili; B. Davvaz

Volume 7, Issue 1 , Summer and Autumn 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 More

4. ON THE REFINEMENT OF THE UNIT AND UNITARY CAYLEY GRAPHS OF RINGS

M. Rezagholibeigi; A. R. Naghipour

Volume 7, Issue 1 , Summer and Autumn 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 More

5. GENERALIZED UNI-SOFT INTERIOR IDEALS IN ORDERED SEMIGROUPS

R. Khan; A. Khan; B. Ahmad; R. Gul

Volume 7, Issue 1 , Summer and Autumn 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 More

6. NEW METHODS FOR CONSTRUCTING GENERALIZED GROUPS, TOPOLOGICAL GENERALIZED GROUPS, AND TOP SPACES

Z. Nazari; A. Delbaznasab; M. Kamandar

Volume 7, Issue 1 , Summer and Autumn 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 More

7. ON THE NORMALITY OF t-CAYLEY HYPERGRAPHS OF ABELIAN GROUPS

R. Bayat; M. Alaeiyan; S. Firouzian

Volume 7, Issue 1 , Summer and Autumn 2019, Pages 95-103

Abstract
  A t-Cayley hypergraph X = t-Cay(G; S) is called normal for a finite group G, if the right regular representationR(G) of G is normal in the full automorphism group Aut(X) of X. In this paper, we investigate the normality of t-Cayley hypergraphs of abelian groups, where S < 4.  Read More