### 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 language | English |
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Pages (from-to) | 1571-1582 |

Number of pages | 12 |

Journal | Communications in Algebra |

Volume | 43 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 3 2015 |

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### 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

*Communications in Algebra*,

*43*(4), 1571-1582. https://doi.org/10.1080/00927872.2013.867969

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

Research output: Contribution to journal › Article

*Communications in Algebra*, vol. 43, no. 4, pp. 1571-1582. https://doi.org/10.1080/00927872.2013.867969

}

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 -