Browsing by Subject "Characteristic polynomial"

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    Factorizations of matrices over projective-free Rings
    (World Scientific Publishing Co. Pte Ltd, 2016) Chen, H.; Kose, H.; Kurtulmaz, Y.
    An element of a ring R is called strongly J#-clean provided that it can be written as the sum of an idempotent and an element in J#(R) that commute. In this paper, we characterize the strong J#-cleanness of matrices over projective-free rings. This extends many known results on strongly clean matrices over commutative local rings. © 2016 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and Suzhou University.
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    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.