Omar Almallah

Al-Balqa Applied University | BAU · Department of Mathematics

A ring is called UU if each its unit is a unipotent. We prove that the group ring R[G] is a commutative UU ring if, and only if, R is a commutative UU ring and G is an abelian 2-group. This extends a result due to McGovern-Raja-Sharp (J. Algebra Appl., 2015) established for commutative nil- clean group rings. In some special cases we also discover...

A commutative ring R with unity is called weakly-présimplifiable (resp., présimplifiable) if for a, b ∈ R with a = ba, then either a = 0 or b is a regular element (that is, b is not a zero-divisor) in R (resp., a = 0 or b is a unit in R). Let R be a commutative ring with unity and G be a nontrivial abelian group. In this paper, we give some charact...

The paper aims to deduce the relation between the category of topology and algebra from viewpoint of geometry and dynamical system. We introduce and define a dynamical manifold as a manifold associated with a time parameter. We obtain the induced chain of topological dynamics on the fundamental group from the chain of dynamical maps on a dynamical...

The commutative ring extensions with exactly two non-Artinian intermediate rings are characterized. An initial step involves the description of the commutative ring extensions with only one non-Artinian intermediate ring. 1. Introduction All rings and algebras considered in this paper are assumed to be commutative with the identity element; all su...

This is the first in a series of papers on the classification of indecomposable QF-rings. Our classification is based on the concepts of a nilary ring and the essentiality of the traces of idempotent generated right ideals. Recall that a ring R is called nilary if AB = 0 then A is nilpotent or B is nilpotent for all ideals A and B of R. In this pap...

A ring is called UU if each its unit is a unipotent. We prove that the group ring R[G] is a commutative UU ring if, and only if, R is a commutative UU ring and G is an abelian 2-group. This extends a result due to McGovern-Raja-Sharp (J. Algebra Appl., 2015) established for commutative nil-clean group rings. In some special cases we also discover w...

A commutative ring R is said to be maximal non-prime ideally equal subring of S, if Spec(R) \(\ne \) Spec(S), whereas Spec(T) \(=\) Spec(S) for any subring T of S properly containing R. The aim of this paper is to give a complete characterization of this class of rings.

In this talk, we characterize a nilary QF-ring R in terms of the essentiality of the ideals ReR where e is a primitive idempotent of R. Recall that a ring R is nilary if AB = 0 implies either A or B is nilpotent for all ideals A and B of R. Note that nilary rings are indecomposable rings.

A commutative ring A is called presimplifiable (respectively, domainlike) if whenever a,b ∈ A with a = ba, then either a = 0 or b is a unit in A (respectively, 0 is a primary ideal of A). Let A be a commutative ring and G be a nonzero abelian group. For the group ring A[G], we prove that if G is torsion, then A[G] is presimplifiable (respectively,...

In a ring $A$ an ideal $I$ is called (principally) nilary if for any two (principal) ideals $V, W$ in $A$ with $VW\subseteq I,$ then either $V^n\subseteq I$ or $W^m\subseteq I,$ for some positive integers $m$ and $n$ depending on $V$ and $W;$ a ring $A$ is called (principally) nilary if the zero ideal is a (principally) nilary ideal~\cite{Birkenmei...

The notions of semi-idempotent elements and nil-semi clean elements are introduced. We show that, if a ring R is a nil-semi clean ring, then the Jacobson radical, J(R), of R is nil. We also characterize some properties related to orthogonal idempotent elements e and f in a ring R. We prove that if R is a nil-semi clean ring and the idempotent eleme...