Additive and product properties of Drazin inverses of elements in a ring

2013/07/27 by Huihui Zhu, Jianlong Chen, Zhu, Huihui +1
Computer Science · Mathematics · #15A09 #16U80 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #math.RA #msc:15A09 #msc:16U80

paper · pdf · doi:10.48550/arxiv.1307.7229

arxiv created 2013/07/27 · openalex publication_date 2013/07/27 · arxiv updated 2013/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Drazin inverses of the sum and product of two elements in a ring. For Drazin invertible elements a and b such that a²b=aba and b²a=bab, it is shown that ab is Drazin invertible and that a+b is Drazin invertible if and only if 1+a^Db is Drazin invertible. Moreover, the formulae of (ab)^D and (a+b)^D are presented. Thus, a generalization of the main result of Zhuang, Chen et al. (Linear Multilinear Algebra 60 (2012) 903-910) is given.

Citations

• Pseudo-Inverses in Associative Rings and Semigroups

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