A note on completeness in the theory of strongly clean rings

Details A note on completeness in the theory of strongly clean rings A note on completeness in the theory of strongly clean rings

2009-07-14

arxiv.org/abs/0907.2281v1

Mathematics

Rings and Algebras

5 pages

Scientific paper

Many authors have investigated the behavior of strong cleanness under certain
ring extensions. In this note, we prove that if $R$ is a ring which is complete
with respect to an ideal $I$ and if $x$ is an element of $R$ whose image in
$R/I$ is strongly $\pi$-regular, then $x$ is strongly clean in $R$.

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