Matrix and Polynomial Reversibility of Rings

Stefan Veldsman

Research output: Contribution to journalArticle

Abstract

Reversibility of rings is a generalization of commutativity, but more than often, this weaker commutativity is a consequence of the absence of certain zero products. For example, a reversible ring is prime if and only if it is an integral domain, and a ring is reduced if and only if it is reversible and semiprime. Here we define and investigate classes of more restricted reversible rings which fulfill stronger commutative requirements, for example, rings that satisfy ab = 0 = ac + db implies ba = 0 = ca + bd.

Original languageEnglish
Pages (from-to)1571-1582
Number of pages12
JournalCommunications in Algebra
Volume43
Issue number4
DOIs
Publication statusPublished - Apr 3 2015

Fingerprint

Reversibility
Ring
Polynomial
Commutativity
If and only if
Integral domain
Imply
Requirements
Zero

Keywords

  • Mat-k-reversible ring
  • Mat-reversible
  • Poly-k-reversible ring
  • Poly-reversible
  • Reversible ring
  • Strongly reversible

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Matrix and Polynomial Reversibility of Rings. / Veldsman, Stefan.

In: Communications in Algebra, Vol. 43, No. 4, 03.04.2015, p. 1571-1582.

Research output: Contribution to journalArticle

Veldsman, Stefan. / Matrix and Polynomial Reversibility of Rings. In: Communications in Algebra. 2015 ; Vol. 43, No. 4. pp. 1571-1582.
@article{db459a8ab73d434ebf7467386d3dc8ea,
title = "Matrix and Polynomial Reversibility of Rings",
abstract = "Reversibility of rings is a generalization of commutativity, but more than often, this weaker commutativity is a consequence of the absence of certain zero products. For example, a reversible ring is prime if and only if it is an integral domain, and a ring is reduced if and only if it is reversible and semiprime. Here we define and investigate classes of more restricted reversible rings which fulfill stronger commutative requirements, for example, rings that satisfy ab = 0 = ac + db implies ba = 0 = ca + bd.",
keywords = "Mat-k-reversible ring, Mat-reversible, Poly-k-reversible ring, Poly-reversible, Reversible ring, Strongly reversible",
author = "Stefan Veldsman",
year = "2015",
month = "4",
day = "3",
doi = "10.1080/00927872.2013.867969",
language = "English",
volume = "43",
pages = "1571--1582",
journal = "Communications in Algebra",
issn = "0092-7872",
publisher = "Taylor and Francis Ltd.",
number = "4",

}

TY - JOUR

T1 - Matrix and Polynomial Reversibility of Rings

AU - Veldsman, Stefan

PY - 2015/4/3

Y1 - 2015/4/3

N2 - Reversibility of rings is a generalization of commutativity, but more than often, this weaker commutativity is a consequence of the absence of certain zero products. For example, a reversible ring is prime if and only if it is an integral domain, and a ring is reduced if and only if it is reversible and semiprime. Here we define and investigate classes of more restricted reversible rings which fulfill stronger commutative requirements, for example, rings that satisfy ab = 0 = ac + db implies ba = 0 = ca + bd.

AB - Reversibility of rings is a generalization of commutativity, but more than often, this weaker commutativity is a consequence of the absence of certain zero products. For example, a reversible ring is prime if and only if it is an integral domain, and a ring is reduced if and only if it is reversible and semiprime. Here we define and investigate classes of more restricted reversible rings which fulfill stronger commutative requirements, for example, rings that satisfy ab = 0 = ac + db implies ba = 0 = ca + bd.

KW - Mat-k-reversible ring

KW - Mat-reversible

KW - Poly-k-reversible ring

KW - Poly-reversible

KW - Reversible ring

KW - Strongly reversible

UR - http://www.scopus.com/inward/record.url?scp=84923269165&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84923269165&partnerID=8YFLogxK

U2 - 10.1080/00927872.2013.867969

DO - 10.1080/00927872.2013.867969

M3 - Article

AN - SCOPUS:84923269165

VL - 43

SP - 1571

EP - 1582

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 4

ER -