One sided polarity along two elements in rings
Abstract
This article examines a way to define the notion of left (right) (b,c)-polar elements in an associative ring R. Necessary and sufficient conditions of an element a∈R to be left (right) (b,c)-polar are investigated. We show that an element a∈R is left (right) (b,c)-polar if and only if a is strongly left (right) (b,c)-invertible. Moreover, the one-sided (b,c)-polarity is characterized in terms of left and right annihilators. As an application, we provide a characterization of the one sided core inverse. Further results and properties are obtained.
Fields of Study & Subjects
Rings
Modules
and Algebras
Finite Group Theory Research
Algebraic structures and combinatorial models
Publication details
- Journal / source
- Linear and Multilinear Algebra
- Publisher
- Informa UK Limited
- Volume
- 74
- Issue
- 10
- Pages
- 1315–1325
- Publication date
- 2 June 2026
- Language
- EN