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An associative ring R with identity is called a clean ring if every element of R is the sum of a unit and an idempotent. In this paper,we introduce the concept of f-clean rings. We study various properties of f-clean rings. [수식]be a Morita Context ring. We determine conditions under which the ring C is f-clean. Moreover, we introduce the concept of rings having many full elements. We investigate characterizations of this kind of rings and show that rings having many full elements are closed under matrix rings and Morita Context rings.
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참고문헌 (19)
참고문헌 신청
A. Haghany / 1999 / Hopficity and co-Hopficity for Morita contexts / Comm. Algebra 27 (1) : 477 ~ 492
D. D. Anderson / 2002 / Commutative rings whose elements are a sum of a unit and idempotent / Comm. Algebra 30 (7) : 3327 ~ 3336
G. Xiao / 2005 / n-clean rings and weakly unit stable range rings / Comm. Algebra 33 (5) : 1501 ~ 1517
H. Chen / 2000 / On stable range conditions / Comm. Algebra 28 (8) : 3913 ~ 3924
H. Chen / 2000 / Rings with many unit-regular elements / Chinese J. Contemp. Math. 21 (1) : 33 ~ 38
D. D. Anderson / 2002 / Commutative rings whose elements are a sum of a unit and idempotent / Comm. Algebra 30 (7) : 3327 ~ 3336
G. Xiao / 2005 / n-clean rings and weakly unit stable range rings / Comm. Algebra 33 (5) : 1501 ~ 1517
H. Chen / 2000 / On stable range conditions / Comm. Algebra 28 (8) : 3913 ~ 3924
H. Chen / 2000 / Rings with many unit-regular elements / Chinese J. Contemp. Math. 21 (1) : 33 ~ 38
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