New characterizations for core inverses in rings with involution
By Sanzhang Xu, Jianlong Chen, Xiaoxiang Zhang. 2015
152 citations recorded by the source corpus.
The core inverse for a complex matrix was introduced by O. M. Baksalary and G. Trenkler. D. S. Rakić, N. Č. Dinčić and D. S. Djordjević 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.
Subfields: Algebra and Number Theory, Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/b3b4e3250354fab18cdef85edb52ac29fad20a1c
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Citations in the corpus
- Pseudo core inverses in rings with involution (2016, background): “© 2018 Taylor & Francis COMMUNICATIONS IN ALGEBRA® 39 Recently, Xu, Chen and Zhang [16] characterized the core invertible elements in R in terms of three equations.”