https://scholars.lib.ntu.edu.tw/handle/123456789/572140
標題: | Inclusion properties of generalized inverses in semiprime rings | 作者: | TSIU-KWEN LEE | 公開日期: | 2021 | 卷: | 20 | 期: | 4 | 來源出版物: | Journal of Algebra and its Applications | 摘要: | Let R be a semiprime ring, not necessarily with unity, with extended centroid C. For a R, let T(a) (respectively I(a), Ref(a)) denote the set of all outer (respectively inner, reflexive) inverses of a in R. In the paper, we study the inclusion properties of T(a), I(a) and Ref(a). Among other results, we prove that for a,b R with a von Neumann regular, Ref(a) T(b) (respectively Ref(a) I(b)) if and only if a = E[a]b (respectively I(a) I(b)). Here, E[a] is the smallest idempotent in C such that E[a]a = a. This gives a common generalization of several known results. ? 2021 World Scientific Publishing Company. |
URI: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85081963009&doi=10.1142%2fS0219498821500572&partnerID=40&md5=7d46eab198dc61558fc2bbd3f5dd2fec https://scholars.lib.ntu.edu.tw/handle/123456789/572140 |
ISSN: | 2194988 | DOI: | 10.1142/S0219498821500572 |
顯示於: | 數學系 |
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