Remark on common properties of the products ac and ba

2021/04/24 by Yanxun Ren, Ren, Yanxun, Lining Jiang +1
Mathematics · #15A09 #47A53 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2104.11862

openalex publication_date 2021/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we discuss the common properties for the products ac and ba in various categories under the condition a(ba)²=abaca=acaba=(ac)²a. We prove that generalized Jacobson's lemma and Cline's formula are suitable for generalized n-strong Drazin invertible in rings, and generalized Jacobson's lemma is suitable for left and right Fredholm operator on Banach spaces.

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