On generalized inverses of regular elements in an arbitrary semiring

Journal of Shanghai Normal University (Natural Sciences)

Wang Qingwen¹  Israr Ali Khan² 

[1] College of Sciences, Shanghai University, Shanghai 200444, China;Department of Electrical Engineering, Namal College, Mianwali, 42250, Pakistan;

关键词: semiring;    regular element;    Moore-Penrose inverse;    Drazin inverse;    group inverse;   

DOI  :  10.3969/J.ISSN.100-5137.2018.03.001

来源: DOAJ

【 摘 要 】

In this paper, we investigate the generalized invertibility for regular elements in an arbitrary semiring. We give some sufficient conditions for the existence of a special kind of {1,2} inverse of a regular element a in an arbitrary semiring and give their expressions. As special cases of this {1,2} inverse, we characterize the Moore-Penrose invertibility and the group invertibility of a.

【 授权许可】

Unknown