New characterizations for core inverses in rings with involution

doi:10.1007/s11464-016-0591-2

Frontiers of Mathematics in China

2017, Vol. 12

Issue (1): 231-246 https://doi.org/10.1007/s11464-016-0591-2

本期目录

New characterizations for core inverses in rings with involution

Sanzhang XU,Jianlong CHEN(

),Xiaoxiang ZHANG

Department of Mathematics, Southeast University, Nanjing 210096, China

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Abstract：

The core inverse for a complex matrix was introduced by O. M. Baksalary and G. Trenkler. D. S. Rakíc, N.Č. Diňcíc and D. S. Djordjevíc generalized the core inverse of a complex matrix to the case of an element in a ring. They also proved that the core inverse of an element in a ring can be characterized by five equations and every core invertible element is group invertible. It is natural to ask when a group invertible element is core invertible. In this paper, we will answer this question. Let R be a ring with involution, we will use three equations to characterize the core inverse of an element. That is, let a, b ∈ R. Then a ∈ R^# with a^# = b if and only if (ab)∗ = ab, ba²= a, and ab²= b. Finally, we investigate the additive property of two core invertible elements. Moreover, the formulae of the sum of two core invertible elements are presented.

Key words： Core inverse dual core inverse group inverse {1,3}-inverse {1,4}-inverse

收稿日期: 2015-11-30 出版日期: 2016-11-17

Corresponding Author(s): Jianlong CHEN

引用本文:

. [J]. Frontiers of Mathematics in China, 2017, 12(1): 231-246.
Sanzhang XU,Jianlong CHEN,Xiaoxiang ZHANG. New characterizations for core inverses in rings with involution. Front. Math. China, 2017, 12(1): 231-246.

链接本文:

https://academic.hep.com.cn/fmc/CN/10.1007/s11464-016-0591-2
https://academic.hep.com.cn/fmc/CN/Y2017/V12/I1/231

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