On a Hereditary Radical Property Relating to the Reducedness

DOI10.1080/00927871003597626zbMath1219.16009OpenAlexW1982611988MaRDI QIDQ3084567

Hong Kee Kim, Yang Lee, Cheong Mi Ha, Nam Kyun Kim, Chan Huh

Publication date: 25 March 2011

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

Full work available at URL: https://doi.org/10.1080/00927871003597626

zbMATH Keywords

nilpotent elementsvon Neumann regular ringssubdirect productsright duo ringsprime radicalAbelian ringsstrongly prime idealsweakly regular ringshereditary radicalsright Ore ringshomomorphically reduced rings

Mathematics Subject Classification ID

Prime and semiprime associative rings (16N60) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Generalizations of commutativity (associative rings and algebras) (16U80) Other classes of modules and ideals in associative algebras (16D80) Ideals in associative algebras (16D25) General radicals and associative rings (16N80) Ore rings, multiplicative sets, Ore localization (16U20) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (2)

Strongly filial rings ⋮ REGULARITY AND STRONG REGULARITY IN THE CONTEXT OF CERTAIN CLASSES OF RINGS

Cites Work

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• Weakly regular rings with ACC on annihilators and maximality of strongly prime ideals of weakly regular rings.
• Exercises in classical ring theory
• Armendariz rings and reduced rings
• On strongly right bounded finite rings
• Structure of minimal noncommutative duo rings and minimal strongly bounded non-duo rings
• Weakly regular rings
• A SIMPLE NIL RING EXISTS
• Rings All of whose Factor Rings are Semi-Prime
• Weakly Regular Rings

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