Commuting $pi$-regular rings

Authors

  • M. Azadi Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Tehran, Iran
  • Sh. Sahebi Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Tehran, Iran
Abstract:

R is called commuting regular ring (resp. semigroup) if for each x,y $in$ R there exists a $in$ R such that xy = yxayx. In this paper, we introduce the concept of commuting $pi$-regular rings (resp. semigroups) and study various properties of them.

full text

similar resources

commuting $pi$-regular rings

r is called commuting regular ring (resp. semigroup) if for each x,y $in$ r thereexists a $in$ r such that xy = yxayx. in this paper, we introduce the concept of commuting$pi$-regular rings (resp. semigroups) and study various properties of them.

full text

Commuting Regular Γ-Semiring

We introduce the notion of commuting regular Γsemiring and discuss some properties of commuting regular Γsemiring. We also obtain a necessary and sufficient condition for Γ-semiring to possess commuting regularity. Keywords—Commutative Γ-semiring, Idempotent Γ-semiring, Rectangular Γ-band, Commuting regular Γ-semiring, Clifford Γsemiring.

full text

Prime rings with PI rings of constants

It is shown that if the ring of constants of a restricted differential Lie algebra with a quasi-Frobenius inner part satisfies a polynomial identity (PI) then the original prime ring has a generalized polynomial identity (GPI). If additionally the ring of constants is semiprime then the original ring is PI. The case of a non-quasi-Frobenius inner part is also considered.

full text

Ore extensions of skew $pi$-Armendariz rings

For a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-Armendariz ring, that is a generalization of both $pi$-Armendariz rings, and $(alpha,delta)$-compatible skew Armendariz rings. We first observe the basic properties of skew $pi$-Armendariz rings, and extend the class of skew $pi$-Armendariz rings through various ring extensions. We nex...

full text

Periodically Regular Chordal Rings

ÐChordal rings have been proposed in the past as networks that combine the simple routing framework of rings with the lower diameter, wider bisection, and higher resilience of other architectures. Virtually all proposed chordal ring networks are nodesymmetric, i.e., all nodes have the same in/out degree and interconnection pattern. Unfortunately, such regular chordal rings are not scalable. In ...

full text

Commuting probability for subrings and quotient rings

We prove that the commuting probability of a finite ring is no larger than the commuting probabilities of its subrings and quotients, and characterize when equality occurs in such a comparison.

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 02  issue 02

pages  67- 70

publication date 2013-06-01

{@ msg @}

By following a journal you will be notified via email when a new issue of this journal is published.

Keywords

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023