2020
DOI: 10.48550/arxiv.2001.08368
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Characterizations of annihilator $(b,c)$-inverses in arbitrary rings

Abstract: In this paper, we investigate some properties of annihilator (b, c)-inverses in an arbitrary ring. We demonstrate that one-sided annihilator (b, c)-inverses of elements in arbitrary rings may behave differently in contrast to one-sided (b, c)-inverses. Also, we discuss intertwining property, absorption law, reverse order law, and Cline's formula for annihilator (b, c)-inverses. As applications, we improve and extend some known results to (b, c)-inverses. In particular, we derive an equivalent condition of inte… Show more

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