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An element in a ring $R$ with identity is called invo-clean if it is the sum of an idempotent and an involution and $R$ is called invo-clean if every element of $R$ is invo-clean. Let $C(R)$ be the center of a ring $R$ and $g(x)$ be a fixed polynomial in $C(R)[x]$. We introduce the new notion of $g(x)$-invo clean. $R$ is called $g(x)$-invo if every element in $R$ is a sum of an involution and a root of $g(x)$. In this paper, we investigate many properties and examples of $g(x)$-invo clean rings. Moreover, we characterize invo-clean as $g(x)$-invo clean rings where $g(x)=(x-a)(x-b)$, $a,b\in C(R)$ and $b-a\in Inv(R)$. Finally, some classes of $g(x)$-invo clean rings are discussed.
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참고문헌 (24)
참고문헌 신청
M. -S. Ahn / 2006 / Weakly clean rings and almost clean rings / Rocky Mountain J. Math 36(3):783~798
M. M. Ali / 2006 / Idealization and theorems of D. D. Anderson / Comm. Algebra 34(12):4479~4501
D. D. Anderson / 2009 / Idealization of a module / J. Commut. Algebra 1(1):3~56
G. Borooah / 2008 / Strongly clean matrix rings over commutative local rings / J. Pure Appl. Algebra 212(1):281~296
V. Camillo / 2002 / The Nicholson-Varadarajan theorem on clean linear transformations / Glasg. Math. J 44(3):365~369
M. M. Ali / 2006 / Idealization and theorems of D. D. Anderson / Comm. Algebra 34(12):4479~4501
D. D. Anderson / 2009 / Idealization of a module / J. Commut. Algebra 1(1):3~56
G. Borooah / 2008 / Strongly clean matrix rings over commutative local rings / J. Pure Appl. Algebra 212(1):281~296
V. Camillo / 2002 / The Nicholson-Varadarajan theorem on clean linear transformations / Glasg. Math. J 44(3):365~369
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