w-核EP逆在对合环上的新刻画

New Characterization of w-Core EP Inverse in Involutive Rings

摘要

考虑对合环上的w-核EP逆,从两个方面讨论其性质.一方面,定义w-核EP分解,通过该分解给出w-核EP逆的新刻画,并讨论w-核EP可逆元的一些新性质.另一方面,通过引入$e=a_{w}^{Ⓓ}(a w)^{k+1}$, $f=wa_{w}^{Ⓓ}(a w)^{k}a$以及投射元$p=awa_{w}^{Ⓓ}$,利用e,f和投射元p对w-核EP核逆进行等价刻画,并由此定义w-核EP序$a\mathop{\le } \limits^Ⓓ{}_{w}b$,研究w-核EP序的性质及其等价刻画.

Abstract

We considered the w-core EP inverse in involutive rings and discussed its properties from two aspects. On the one hand, the w-core EP decomposition was defined, and a new characterization of the w-core EP inverse was given through the w-core EP decomposition, and some new properties of the w-core EP invertible element were discussed. On the other hand, $e=a_{w}^{Ⓓ}(a w)^{k+1}$, $f=wa_{w}^{Ⓓ}(a w)^{k}a$ and the projection element $p=awa_{w}^{Ⓓ}$ were introduced. The w-core EP core inverse was equivalently characterized by using e, f and the projection element p, and the w-core EP order $a\mathop{\le } \limits^Ⓓ{}_{w}b$ was defined accordingly. The properties and its equivalent characterizations of the w-core EP order were studied.

关键词

w-核逆 / w-核EP逆 / w-核EP分解 / w-核EP序

Key words

w-core inverse / w-core EP inverse / w-core EP decomposition / w-core EP order

参考文献

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基金资助

安徽省自然科学基金(2008085MA06)

安徽省教育厅重点研究项目(KJ2019A0488)