NORMAL PAIRS WITH ZERO-DIVISORS

DOI10.1142/S0219498811004628zbMath1221.13012OpenAlexW2103155026MaRDI QIDQ3006047

Jay Shapiro, David E. Dobbs

Publication date: 10 June 2011

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219498811004628

zbMATH Keywords

regular elementsvon Neumann regular ringsreduced ringsoverringsintegrally closed ringstotal quotient ringsnormal pairs of ringsregular divided prime ideal

Mathematics Subject Classification ID

Integral domains (13G05) Ideals and multiplicative ideal theory in commutative rings (13A15) Extension theory of commutative rings (13B02) Integral dependence in commutative rings; going up, going down (13B21) Other special types of modules and ideals in commutative rings (13C13) Rings of fractions and localization for commutative rings (13B30)

Related Items (18)

On Finite Maximal Chains of Weak Baer Going-Down Rings ⋮ An answer to a question about maximal non-integrally closed subrings ⋮ Normal pairs of noncommutative rings ⋮ Maximal non-integrally closed subrings of an integral domain ⋮ Unnamed Item ⋮ Characterizing the ring extensions that satisfy FIP or FCP ⋮ New results about normal pairs of rings with zero-divisors ⋮ Maximal non $\lambda$-subrings ⋮ Ring extensions with finitely many non-Artinian intermediate rings ⋮ On almost valuation ring pairs ⋮ On the commutative ring extensions with at most two non Prüfer intermediate rings ⋮ Some results about proper overrings of pseudo-valuation domains ⋮ A note on imbedded prime divisors ⋮ Pointwise maximal subrings ⋮ THE FERRAND-OLIVIER CLASSIFICATION OF THE MINIMAL RING EXTENSIONS OF A FIELD: A PROOF AND A SURVEY OF ITS INFLUENCE ⋮ Finite maximal chains of commutative rings ⋮ A GENERALIZATION OF PRÜFER'S ASCENT RESULT TO NORMAL PAIRS OF COMPLEMENTED RINGS ⋮ Generalized normality in ring extensions involving amalgamated algebras

Cites Work

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• A construction of Gorenstein rings
• Topologically defined classes of commutative rings
• Divided rings and going-down
• Prime ideals in ultraproducts of commutative rings
• AN AMALGAMATED DUPLICATION OF A RING ALONG AN IDEAL: THE BASIC PROPERTIES
• A Generalization of Divided Domains and Its Connection to Weak Baer Going-Down Rings
• DIVISIBILITY CONDITIONS IN COMMUTATIVE RINGS WITH ZERODIVISORS
• Irreducibility in the Total Ring of Quotients
• Remarks on generalized rings of quotients
• A Characterization of Prüfer Domains

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