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- W1680358081 abstract "An element $a$ of a ring $R$ is called emph{quasipolar} provided that there exists an idempotent $pin R$ such that $pin comm^2(a)$, $a+pin U(R)$ and $apin R^{qnil}$. A ring $R$ is emph{quasipolar} in case every element in $R$ is quasipolar. In this paper, we investigate quasipolarity of generalized matrix rings $K_s (R)$ for a commutative local ring $R$ and $sin R$. We show that if $s$ is nilpotent, then $K_s(R)$ is quasipolar. We determine the conditions under which elements of $K_s (R)$ are quasipolar. It is shown that $K_s(R)$ is quasipolar if and only if $tr(A)in J(R)$ or the equation $x^2-tr(A)x+det_s(A)=0$ is solvable in $R$ for every $Ain K_s(R)$ with $det_s(A)in J(R)$. Furthermore, we prove that $M_2(R)$ is quasipolar if and only if $M_2(R)$ is strongly clean for a commutative local ring $R$." @default.
- W1680358081 created "2016-06-24" @default.
- W1680358081 creator A5057004244 @default.
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- W1680358081 date "2013-03-13" @default.
- W1680358081 modified "2023-10-18" @default.
- W1680358081 title "Quasipolarity of Generalized Matrix Rings" @default.
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