### 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 |

### 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

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## Cite this

Veldsman, S. (2015). Matrix and Polynomial Reversibility of Rings.

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