Conducive integral domains

DOI10.1016/0021-8693(84)90044-9zbMath0531.13002OpenAlexW2067350517MaRDI QIDQ788053

David E. Dobbs, Richard Fedder

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1016/0021-8693(84)90044-9

zbMATH Keywords

Prüfer domainpullbackG-domainsconducive domainseminormal domain\(D+M\) constructionsmaximum overringnonzero conductor of overringpinched spectrumpseudo-valuation domains

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18) Integral domains (13G05) Extension theory of commutative rings (13B02) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15) Rings of fractions and localization for commutative rings (13B30)

Related Items (43)

Strongly divisorial ideals and complete integral closure of an integral domain ⋮ Krull Dimension in Power Series Ring Over an Almost Pseudo-Valuation Domain ⋮ POWERFUL IDEALS, STRONGLY PRIMARY IDEALS, ALMOST PSEUDO-VALUATION DOMAINS, AND CONDUCIVE DOMAINS ⋮ Gorenstein conducive domains ⋮ Ahmes expansions of formal Laurent series and a class of nonarchimedean integral domains ⋮ RATLIFF–RUSH CLOSURE OF IDEALS IN INTEGRAL DOMAINS ⋮ Unnamed Item ⋮ G-domains and spectral spaces ⋮ A note on linear topologies ⋮ Coherent mori domains and the principal ideal theorem ⋮ Class semigroups of integral domains ⋮ Fuzzy semistar operations on overrings ⋮ On the cardinality of star operations on a pseudo-valuation domain ⋮ Multiplicative closure operations on ring extensions ⋮ Noetherian domains in which every ideal is isomorphic to a trace ideal ⋮ Corps des fractions de AX ⋮ When is the dual of an ideal a ring? ⋮ On some classes of integral domains defined by Krull's \(a.b.\) operations ⋮ Note on the divisoriality of domains of the form $k[[X^{p}, X^{q}]$, $k[X^{p}, X^{q}]$, $k[[X^{p}, X^{q}, X^{r}]]$, and $k[X^{p}, X^{q}, X^{r}]$] ⋮ On the Cardinality of Semistar Operations on Integral Domains ⋮ ES-w-stability ⋮ Unnamed Item ⋮ Semistar-operations of finite character on integral domains ⋮ About the quotient fields of formal power series domains ⋮ On the set of \(t\)-linked overrings of an integral domain ⋮ A localization of a power series ring over a Prüfer domain ⋮ Straight Rings ⋮ A class of integral domains whose integral closures are small submodules of the quotient field ⋮ Integral Domains in Which Each Ideal Is aW-Ideal ⋮ Star Operations on Overrings and Semistar Operations ⋮ Locally pseudo-valuation domains with only finitely many star operations ⋮ Constituent groups of Clifford semigroups arising from \(t\)-closure ⋮ Krull dimension, overrings and semistar operations of an integral domain ⋮ Stability in Commutative Rings ⋮ Some classification of certain integral domains via conductor overrings and semistar operations ⋮ Ratliff–Rush Closure of Ideals in Pullbacks and Polynomial Rings ⋮ Integrally Closed Domains with Only Finitely Many Star Operations ⋮ Finitely star regular domains ⋮ Semistar Operations and Standard Closure Operations ⋮ INTEGRAL AND COMPLETE INTEGRAL CLOSURES OF IDEALS IN INTEGRAL DOMAINS ⋮ Note on the stability of a presemistar operation ⋮ Graded powerful ideals in a graded integral domain ⋮ Conducive integral domains as pullbacks

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On \(\text{Pic}(R[X)\) for \(R\) seminormal]
• Topologically defined classes of commutative rings
• Divided rings and going-down
• The pseudo-radical of a commutative ring
• Overrings and divisorial ideals of rings of the form \(D+M\)
• Two conductor theorems
• Remarks on module-finite pairs
• On seminormal overrings
• Pairs of Rings with the Same Prime Ideals
• Some Counterexamples Related to Integral Closure in x
• On Going Down for Simple Overrings
• La Notion D’anneau de Décomposition

This page was built for publication: Conducive integral domains