Some properties of (b, c)-inverses in rings

In this paper, we study (b, c)-invertibility of some arbitrary (b, c)-inverse and we give an equivalent condition for its (b, c)-invertibility. Moreover, we investigate when some well known properties of generalized inverses hold for (b, c)-inverses. Further, we study when the (b, c)-inverse of the...

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Bibliographic Details
Published in:Communications in algebra 2023-06, Vol.51 (6), p.2600-2613
Main Authors: Višnjić, Jelena, Stanišev, Ivana, Ke, Yuanyuan
Format: Article
Language:English
Subjects:
c)-Inverse
commuting properties
Equivalence
generalized inverse
Multiplication
reverse order law
Unity
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Summary:In this paper, we study (b, c)-invertibility of some arbitrary (b, c)-inverse and we give an equivalent condition for its (b, c)-invertibility. Moreover, we investigate when some well known properties of generalized inverses hold for (b, c)-inverses. Further, we study when the (b, c)-inverse of the unity is equal to the unity itself and we obtain equivalent conditions for this to hold. In addition, we investigate the reverse order law for the (b, c)-inverse. Finally, we prove that in the case when the unity is (b, c)-invertible, the set of all (b, c)-inverses, with respect to multiplication, is a group.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2023.2166947