Almost unit-clean rings

buir.contributor.author	Kurtulmaz, Yosum
dc.citation.epage	121	en_US
dc.citation.issueNumber	1	en_US
dc.citation.spage	113	en_US
dc.citation.volumeNumber	21	en_US
dc.contributor.author	Chen, H.	en_US
dc.contributor.author	Köse, H.	en_US
dc.contributor.author	Kurtulmaz, Yosum	en_US
dc.date.accessioned	2020-02-18T13:10:56Z
dc.date.available	2020-02-18T13:10:56Z
dc.date.issued	2019
dc.department	Department of Mathematics	en_US
dc.description.abstract	A ring R is almost unit-clean provided that every element in R is equivalent to the sum of an idempotent and a regular element. We investigate conditions under which a ring is almost unit-clean. We prove that every ring in which every zero-divisor is strongly _-regular is almost unit-clean and every matrix ring of elementary divisor domains is almost unit-clean. Furthermore, it is shown that the trivial extension R(M) of a commutative ring R and an R-module M is almost unit-clean if and only if each x 2 R can be written in the form ux = r+e where u 2 U(R); r 2 R 􀀀 (Z(R) [ Z(M)) and e 2 Id(R). We thereby construct many examples of such rings.	en_US
dc.identifier.issn	1582-3067
dc.identifier.uri	http://hdl.handle.net/11693/53418
dc.language.iso	English	en_US
dc.publisher	Editura Academiei Romane	en_US
dc.source.title	Mathematical Reports	en_US
dc.subject	Almost unit-clean ring	en_US
dc.subject	Elementary divisor ring	en_US
dc.subject	Strongly π-regular ring	en_US
dc.title	Almost unit-clean rings	en_US
dc.type	Article	en_US

Files

Now showing 1 - 1 of 1

Now showing 1 - 1 of 1