A recursive construction of units in a class of rings

F. D. de Melo Hernandez; César A. Hernández Melo; Horacio Tapia-Recillas

A recursive construction of units in a class of rings

Rings and Algebras 2020-04-30 v2

Authors: F. D. de Melo Hernandez , César A. Hernández Melo , Horacio Tapia-Recillas

Abstract

Let $R$ be an associative ring with identity and let $N$ be a nil ideal of $R$ . It is shown that units of $R/N$ can be lifted to units in $R$ . Under some mild conditions on the ring, a procedure is given to determine those lifted units in a recursive way. As an application, the units of several classes of rings are determined, including: matrix rings, chain rings, and group rings where the ring is a chain ring. Numerical examples are given illustrating the main results.

Keywords

associative ring nil ideal unit lifting recursive construction matrix ring chain ring group ring

Cite

@article{arxiv.1911.07743,
  title  = {A recursive construction of units in a class of rings},
  author = {F. D. de Melo Hernandez and César A. Hernández Melo and Horacio Tapia-Recillas},
  journal= {arXiv preprint arXiv:1911.07743},
  year   = {2020}
}

Comments

arXiv admin note: text overlap with arXiv:1904.12932 corrected typos

A recursive construction of units in a class of rings

Abstract

Keywords

Cite

Comments

Related papers