Group, Moore–Penrose, core and dual core inverse in rings with involution☆
Group, Moore–Penrose, core and dual core inverse in rings with involution☆
复制标题
DOI：
10.1016/j.laa.2014.09.003
复制
发表时间：
2014-03
影响因子：
1.1
通讯作者：
Dragan S. Raki'c;Nebojvsa vC. Dinvci'c;Dragan S. Djordjevi'c
中科院分区：
文献类型：
--
作者：
Dragan S. Raki'c;Nebojvsa vC. Dinvci'c;Dragan S. Djordjevi'c
设R是具有对合的环。最近引进的核心和对偶核心逆的概念，从矩阵推广到任意的双-环的情况。证明了群、Moore-Penrose、核和对偶核逆是密切相关的，它们可以用适当的幂等元以同样的方式处理。给出了这些逆的几个特征。得到了一些新的性质，推广了一些已知的结果。得到了R中EP元的若干特征。证明了核和对偶核逆属于逆类沿着元素和（B，c）-逆类.
Let R be a ring with involution. The recently introduced notions of the core and dual core inverse are extended from matrix to an arbitrary⁎-ring case. It is shown that the group, Moore–Penrose, core and dual core inverse are closely related and they can be treated in the same manner using appropriate idempotents. The several characterizations of these inverses are given. Some new properties are obtained and some known results are generalized. A number of characterizations of EP elements in R are obtained. It is shown that core and dual core inverse belong to the class of inverses along an element and to the class of (b, c)-inverses.