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arXiv · 1911.07743

A recursive construction of units in a class of rings

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

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F. D. de Melo Hernandez, César A. Hernández Melo, Horacio Tapia-Recillas. 2020-04-29. A recursive construction of units in a class of rings. https://arxiv.org/abs/1911.07743

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