Browsing by Subject "Very J-clean ring"
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Item Open Access Very cleanness of generalized matrices(Springer, 2016-01) Kurtulmaz, Y.An element a in a ring R is very clean in case there exists an idempotent e 2 R such that ae = ea and either a e or a + e is invertible. An element a in a ring R is very J-clean provided that there exists an idempotent e 2 R such that ae = ea and either ae 2 J(R) or a + e 2 J(R). Let R be a local ring, and let s 2 C(R). We prove that A 2 Ks(R) is very clean if and only if A 2 U(Ks(R)); I A 2 U(Ks(R)) or A 2 Ks(R) is very J-clean.