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A *-ring R is called (strongly) *-clean if every element of R is the sum of a projection and a unit (which commute with each other). In this note, some properties of *-clean rings are considered. In particular, a new class of *-clean rings which called strongly π-*-regular are introduced. It is shown that R is strongly π-*-regular if and only if R is π-regular and every idempotent of R is a projection if and only if R/J(R) is strongly regular with J(R) nil, and every idempotent of R/J(R) is lifted to a central projection of R. In addition, the stable range conditions of *-clean rings are discussed, and equivalent conditions among *-rings related to *-cleanness are obtained.
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참고문헌 (16)
참고문헌 신청
A. Badawi / 1997 / On abelian -regular rings / Comm. Algebra 25 (4) : 1009 ~ 1021
A. Y. M. Chin / 2002 / On strongly π-regular group rings / Southeast Asian Bull. Math 26 (3) : 387 ~ 390
C. Li / 2011 / On strongly *-clean rings / J. Algebra Appl 10 (6) : 1363 ~ 1370
G. Borooah / 2008 / Strongly clean matrix rings over commutative local rings / J. Pure Appl. Algebra 212 (1) : 281 ~ 296
H. Chen / 1999 / Rings with many idempotents / Int. J. Math. Math. Sci 22 (3) : 547 ~ 558
A. Y. M. Chin / 2002 / On strongly π-regular group rings / Southeast Asian Bull. Math 26 (3) : 387 ~ 390
C. Li / 2011 / On strongly *-clean rings / J. Algebra Appl 10 (6) : 1363 ~ 1370
G. Borooah / 2008 / Strongly clean matrix rings over commutative local rings / J. Pure Appl. Algebra 212 (1) : 281 ~ 296
H. Chen / 1999 / Rings with many idempotents / Int. J. Math. Math. Sci 22 (3) : 547 ~ 558
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