Browsing by Subject "Local ring"

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    Strongly j-clean skew triangular matrix rings
    (Universitatea "Alexandru Ioan Cuza" din Iasi * Facultatea de Matematica,"Alexandru Ioan Cuza" University of Iasi, Faculty of Mathematics, 2016-02-06) Kurtulmaz, Y.
    Let R be an arbitrary ring with identity. An element a 2 R is strongly J-clean if there exist an idempotent e 2 R and element w 2 J(R) such that a = e + w and ew = ew. A ring R is strongly J-clean in case every element in R is strongly J-clean. In this note, we investigate the strong J-cleanness of the skew triangular matrix ring Tn(R, ) over a local ring R, where is an endomorphism of R and n = 2, 3, 4.
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    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 a􀀀e 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.