Negative clean rings

Călugăreanu, Grigore; Pop, Horia F.

doi:10.2478/auom-2022-0019

Abstract

A ring is called negative clean if the negative (i.e., the additive inverse) of each clean element is also clean. Clean rings are negative clean.

In this paper, we develop the theory of the negative rings, with special emphasis on finding the clean matrices which have (or have not) clean negatives. Many explicit results are proved for 2 × 2 matrices and some hard to solve quadratic Diophantive equations are displayed.

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Negative clean rings

Abstract

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