June 2023 THE POLARITY ALONG AN ELEMENT IN RINGS
Yaoyao Song, Huihui Zhu, Dijana Mosić
Rocky Mountain J. Math. 53(3): 937-949 (June 2023). DOI: 10.1216/rmj.2023.53.937

Abstract

Let R be a ring with unity 1. We introduce the definition of the (dual) polarity along an element in R. Given any a,dR, an element a is polar along d if there exists some pR such that p2=pcomm(da), pd=d and da+1p is a unit. Also, the dual polarity along an element is given. Simply polar elements, polar elements and well-supported elements are special cases of polar elements along d. Moreover, several properties and characterizations of the polarity along an element are investigated.

Citation

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Yaoyao Song. Huihui Zhu. Dijana Mosić. "THE POLARITY ALONG AN ELEMENT IN RINGS." Rocky Mountain J. Math. 53 (3) 937 - 949, June 2023. https://doi.org/10.1216/rmj.2023.53.937

Information

Received: 8 January 2022; Revised: 3 June 2022; Accepted: 27 June 2022; Published: June 2023
First available in Project Euclid: 21 July 2023

MathSciNet: MR4617922
zbMATH: 07731156
Digital Object Identifier: 10.1216/rmj.2023.53.937

Subjects:
Primary: 16U60 , 16W10

Keywords: Drazin inverses , group inverses , inverses along an element , Moore–Penrose inverses , polar elements , well-supported elements

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.53 • No. 3 • June 2023
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