t-class semigroups of integral domains

DOI10.1515/CRELLE.2007.088zbMath1151.13003arXivmath/0606636OpenAlexW2756816365MaRDI QIDQ5459213

Abdeslam Mimouni, Salah-Eddine Kabbaj

Publication date: 25 April 2008

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0606636

zbMATH Keywords

Prüfer \(v\)-multiplication domainPVMD\(t\)-class semigroup

Mathematics Subject Classification ID

Ideals and multiplicative ideal theory in commutative rings (13A15) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Semigroups (20M99) Theory of modules and ideals in commutative rings (13C99)

Related Items (23)

Duals and Transforms of Ideals in PVMDs ⋮ Minimal reductions and core of ideals in pullbacks ⋮ Core of ideals in one-dimensional Noetherian domains ⋮ Integral domains with Boolean \(t\)-class semigroup ⋮ Finitely Stable Rings ⋮ Flat ideals and stability in integral domains ⋮ Core of ideals in integral domains ⋮ Integral domains of finite \(t\)-character ⋮ Reductions and cores of ideals in trivial ring extensions ⋮ Structure of general ideal semigroups of monoids and domains ⋮ Reductions and Core of Ideals in Integral Domains: Some Recent Developments ⋮ On locally AGCD domains ⋮ Semigroup rings as weakly factorial domains, II ⋮ Star stability and star regularity for Mori domains ⋮ Integral Domains in Which Nonzero Locally Principal Ideals are Invertible ⋮ Unnamed Item ⋮ Graded Prüfer domains with Clifford homogeneous class semigroups ⋮ w-Divisoriality in Polynomial Rings ⋮ Constituent groups of Clifford semigroups arising from \(t\)-closure ⋮ Clifford semigroups of ideals in monoids and domains ⋮ Unique factorization property of non-unique factorization domains ⋮ Generic formal fibers and analytically ramified stable rings ⋮ w-Stability and Cliffordw-Regularity of Polynomial Rings

Cites Work

• Strongly divisorial ideals and complete integral closure of an integral domain
• On divisorial prime ideals in Prüfer v-multiplication domains
• Prüfer v-multiplication domains and the ring \(R[X_{N_ v}\)]
• Integral domains in which each t-ideal is divisorial
• Idéaux divisoriels d'un anneau de polynômes
• When the dual of an ideal is a ring
• Almost Bézout domains
• \(D+M\) constructions with general overrings
• Globalizing local properties of Prüfer domains
• On strong Mori domains
• Coherentlike conditions in pullbacks
• Class semigroups of integral domains
• Groups in the class semigroups of valuation domains
• On the class group and the local class group of a pullback
• Class semigroups of Prüfer domains
• When is the dual of an ideal a ring?
• Prüfer domains and endomorphism rings of their ideals
• Overrings and divisorial ideals of rings of the form \(D+M\)
• t-Linked overrings and prüfer v-multiplication domains
• On t-invertibility
• When is D + M Coherent?
• Pairs of Rings with the Same Prime Ideals
• Pseudo-Integrality
• The class semigroup of orders in number fields
• Groups in the class semigroup of a prüfer domain of finite character
• ON THE STRUCTURE OF STABLE DOMAINS
• ON A CLASS OF PRUFER -MULTIPLICATION DOMAINS
• Some Results on v-Multiplication Rings
• Stable Ideals and Arf Rings
• Stable rings and a problem of Bass
• Clifford regular domains
• On the classification of stable domains

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