Rings in which not invertible elements are uniquely clean
نویسندگان
چکیده
We call a ring R generalized uniquely clean (or GUC for short) if every not invertible element in is clean. Let be ring. It shown that and only it local or Thus the generalization of Some basic properties rings are proved.
منابع مشابه
Uniquely Clean Elements in Rings
It is well known that every uniquely clean ring is strongly clean. In this paper, we investigate the question of when this result holds element-wise. We first construct an example showing that uniquely clean elements need not be strongly clean. However, in case every corner ring is clean the uniquely clean elements are strongly clean. Further, we classify the set of uniquely clean elements for ...
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متن کاملrings in which elements are the sum of an idempotent and a regular element
let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents...
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ژورنال
عنوان ژورنال: Bulletin of the "Transilvania" University of Bra?ov
سال: 2023
ISSN: ['2344-2034', '2344-2026']
DOI: https://doi.org/10.31926/but.mif.2023.3.65.1.12