A Generalization of Divided Domains and Its Connection to Weak Baer Going-Down Rings

DOI10.1080/00927870902828488zbMath1200.13017OpenAlexW2024605604MaRDI QIDQ3646338

Jay Shapiro, David E. Dobbs

Publication date: 20 November 2009

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

Full work available at URL: https://doi.org/10.1080/00927870902828488

zbMATH Keywords

pullbackoverringvon Neumann regular ringintegralitytotal quotient ringreduced ringregular elementMarot ringweak Baer ringextensionally going-down ringregular divided prime idealregular comparable ringregular quotient ring

Mathematics Subject Classification ID

Integral domains (13G05) Ideals and multiplicative ideal theory in commutative rings (13A15) Integral dependence in commutative rings; going up, going down (13B21) Other special types of modules and ideals in commutative rings (13C13) Commutative ring extensions and related topics (13B99)

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Cites Work

• Unnamed Item
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• Topologically defined classes of commutative rings
• Seminormal or \(t\)-closed schemes and Rees rings
• ON LOCALLY DIVIDED RINGS AND GOING-DOWN RINGS
• Universal Lying-Over Rings
• CPI-Extensions: Overrings of Integral Domains with Special Prime Spectrums
• On divided commutative rings
• On Going Down For Simple Overrings II
• Anneauxt-clos
• Irreducibility in the Total Ring of Quotients
• On seminormality