Generalizing unit-regular rings and special clean elements

DOI10.22199/issn.0717-6279-2020-05-0069zbMath1489.16040OpenAlexW3089957955MaRDI QIDQ5018658

Peter V. Danchev

Publication date: 21 December 2021

Published in: Proyecciones (Antofagasta) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.22199/issn.0717-6279-2020-05-0069

zbMATH Keywords

clean ringsunit-regular ringsweakly clean ringsweakly unit-regular ringsspecial clean elements

Mathematics Subject Classification ID

Ideals and multiplicative ideal theory in commutative rings (13A15) Conditions on elements (16U99)

Cites Work

• Weakly clean rings.
• Generalizing \(\pi\)-regular rings
• A note on weakly clean rings.
• A note on the group structure of unit regular ring elements
• Perspectivity and cancellation in regular rings
• Exercises in classical ring theory.
• Generalizing nil clean rings
• Weakly-Abel rings and weakly exchange rings.
• On a class of regular rings that are elementary divisor rings
• EXTENSIONS OF CLEAN RINGS
• A CHARACTERIZATION OF UNIT REGULAR RINGS
• Corner Rings of a Clean Ring Need Not be Clean
• On Almost Unit-Regular Rings
• Lifting Idempotents and Exchange Rings
• Unit regular elements in corner rings
• Strongly clean rings and fitting's lemma
• Connections between unit-regularity, regularity, cleanness, and strong cleanness of elements and rings
• Special clean elements in rings
• Examples of strongly clean rings
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