Hybrid (b, c)-inverses and five finiteness properties in rings, semigroups, and categories

DOI10.1080/00927872.2020.1869246zbMath1485.16002OpenAlexW3125029055MaRDI QIDQ5858472

Michael P. Drazin

Publication date: 13 April 2021

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927872.2020.1869246

zbMATH Keywords

ringsemigroupcategorygeneralized inverseannihilatorouter inversestrong \(\pi\)-regularityfiniteness condition\((b, c)\)-inversehybrid \((b, c)\)-inverse

Mathematics Subject Classification ID

Ideal theory for semigroups (20M12) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Chain conditions, growth conditions, and other forms of finiteness for associative rings and algebras (16P99) Other classes of modules and ideals in associative algebras (16D80) General theory of categories and functors (18A99) General and miscellaneous (16B99) Generalized inverses (associative rings and algebras) (16U90)

Related Items (5)

A new class of generalized inverses in semigroups and rings with involution ⋮ A class of outer generalized inverses and a note on Drazin’s finiteness conditions in rings and semigroups ⋮ The \((b, c)\)-core inverse and its dual in semigroups with involution ⋮ Unnamed Item ⋮ Weighted (b,c)-inverses in categories and semigroups

Cites Work

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• Left and right generalized inverses
• Bass's first stable range condition
• Generalized inverses. Theory and applications.
• A class of outer generalized inverses
• \(K\)-theory and stable algebra
• Strongly 𝜋-regular rings have stable range one
• Further results on several types of generalized inverses

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