Browsing by Subject "Strongly clean matrix"
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Item Open Access Certain clean decompositions for matrices over local rings(Kyungpook National University Department of Mathematics, 2023-12-31) Kurtulmaz, Yosum ; Köse, Handan; Chen, HuanyinAn element a E R is strongly rad-clean provided that there exists an idempotent e E R such that a -e E U(R), ae = ea and eae E J(eRe). In this article, we completely determine when a 2 x 2 matrix over a commutative local ring is strongly rad clean. An application to matrices over power-series is also given.Item Open Access Strongly clean matrices over power series(Kyungpook National University, 2016) Chen, H.; Kose, H.; Kurtulmaz, Y.An n × n matrix A over a commutative ring is strongly clean provided that it can be written as the sum of an idempotent matrix and an invertible matrix that commute. Let R be an arbitrary commutative ring, and let A(x) ∈ Mn ( R[[x]]) . We prove, in this note, that A(x) ∈ Mn ( R[[x]]) is strongly clean if and only if A(0) ∈ Mn(R) is strongly clean. Strongly clean matrices over quotient rings of power series are also determined.