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Pseudopolarity of Generalized Matrix Rings over a Local Ring

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【作者】 Yin Xiao-binDou WanDu Xian-kun

【Author】 Yin Xiao-bin;Dou Wan;Du Xian-kun;College of Mathematics and Computer Science, Anhui Normal University;

【机构】 College of Mathematics and Computer Science, Anhui Normal University

【摘要】 Pseudopolar rings are closely related to strongly π-regular rings, uniquely strongly clean rings and semiregular rings. In this paper, we investigate pseudopolarity of generalized matrix rings K s(R) over a local ring R. We determine the conditions under which elements of K s(R) are pseudopolar. Assume that R is a local ring. It is shown that A ∈ K s(R) is pseudopolar if and only if A is invertible or A2∈ J(K s(R)) or A is similar to a diagonal matrix[u 00 j], where l u-r j and l j-r u are injective and u ∈ U(R) and j ∈ J(R). Furthermore, several equivalent conditions for K s(R)over a local ring R to be pseudopolar are obtained.

【基金】 The NSF(10871024,11326062) of China
  • 【DOI】10.13447/j.1674-5647.2015.03.03
  • 【分类号】O153.3
  • 【被引频次】2
  • 【下载频次】27
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