Pseudopolar rings are closely related to strongly -regular rings, uniquelystrongly clean rings and semiregular rings. In this paper, we investigate pseudopolar-ity of generalized matrix rings Ks(R) over a local ring...Pseudopolar rings are closely related to strongly -regular rings, uniquelystrongly clean rings and semiregular rings. In this paper, we investigate pseudopolar-ity of generalized matrix rings Ks(R) over a local ring R. We determine the conditionsunder which elements of Ks(R) are pseudopolar. Assume that R is a local ring. It isshown that A ∈ Ks(R) is pseudopolar if and only if A is invertible or A^2 ∈ J(Ks(R))or A is similar to a diagonal matrix [ u 0 0 j ]; where lu -rj and lj-ru are injectiveand u 2 U(R) and j ∈ J(R). Furthermore, several equivalent conditions for Ks(R)over a local ring R to be pseudopolar are obtained.展开更多
文摘Pseudopolar rings are closely related to strongly -regular rings, uniquelystrongly clean rings and semiregular rings. In this paper, we investigate pseudopolar-ity of generalized matrix rings Ks(R) over a local ring R. We determine the conditionsunder which elements of Ks(R) are pseudopolar. Assume that R is a local ring. It isshown that A ∈ Ks(R) is pseudopolar if and only if A is invertible or A^2 ∈ J(Ks(R))or A is similar to a diagonal matrix [ u 0 0 j ]; where lu -rj and lj-ru are injectiveand u 2 U(R) and j ∈ J(R). Furthermore, several equivalent conditions for Ks(R)over a local ring R to be pseudopolar are obtained.