JP Journal of Algebra, Number Theory and Applications
Volume 46, Issue 2, Pages 165 - 179
(May 2020) http://dx.doi.org/10.17654/NT046020165 |
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CHARACTERIZATIONS OF ANNIHILATOR (b, c)-INVERSES IN ARBITRARY RINGS
Chong-Quan Zhang, Fujia Chang and Heng Gao
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Abstract: In this paper, we extend the notion of annihilator (b, c)-inverses to arbitrary rings (not necessary with identity). Then we demonstrate that annihilator (b, c)-inverses of elements in arbitrary rings may behave differently in contrast to (b, c)-inverses in semigroups. Further connections between annihilator (b, c)-inverses and one-sided ones are also investigated. In addition, we obtain a new general case of bicommutant property for annihilator (b, c)-inverses. As a consequence, we show that and together imply where is the Moore-Penrose inverse of a in a *-ring. |
Keywords and phrases: generalized inverse, one-sided inverse, bicommutant.
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