Clifford semigroups of ideals in monoids and domains

DOI10.1515/FORUM.2009.050zbMath1189.13002MaRDI QIDQ3401173

Franz Halter-Koch

Publication date: 29 January 2010

Published in: Forum Mathematicum (Search for Journal in Brave)

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (27)

The \(t\)-Nagata ring of \(t\)-Schreier domains ⋮ \(t\)-invertibility and Bazzoni-like statements ⋮ Integral domains with Boolean \(t\)-class semigroup ⋮ Ten Problems on Stability of Domains ⋮ Open Problems in Commutative Ring Theory ⋮ Flat ideals and stability in integral domains ⋮ Core of ideals in integral domains ⋮ Integral domains of finite \(t\)-character ⋮ Structure of general ideal semigroups of monoids and domains ⋮ Reductions and Core of Ideals in Integral Domains: Some Recent Developments ⋮ A Bazzoni-Type Theorem for Multiplicative Lattices ⋮ A Survey on the Local Invertibility of Ideals in Commutative Rings ⋮ Semigroup rings as weakly factorial domains, II ⋮ Bazzoni’s conjecture and almost Prüfer domains ⋮ Star stability and star regularity for Mori domains ⋮ Graded Prüfer domains ⋮ t-Schreier Domains ⋮ Integral Domains in Which Nonzero Locally Principal Ideals are Invertible ⋮ On LPI rings ⋮ LPIdomains and Pullbacks ⋮ Finite character of finitely stable domains ⋮ A characterization of seminormal C-monoids ⋮ Graded Prüfer domains with Clifford homogeneous class semigroups ⋮ w-Stability and Cliffordw-Regularity of Polynomial Rings ⋮ Integral Domains in which Every Nonzerot-Locally Principal Ideal ist-Invertible ⋮ On \(\star\)-potent domains and \(\star\)-homogeneous ideals ⋮ Stability and Clifford Regularity with Respect to Star Operations

Cites Work

• Ideal semigroups of noetherian domains and Ponizovski decompositions
• Class semigroups of integral domains
• Groups in the class semigroups of valuation domains
• Class semigroups of Prüfer domains
• On the theory of orders, in particular on the semigroup of ideal classes and genera of an order in an algebraic number field
• A general theory of class groups
• The class semigroup of orders in number fields
• The hierarchy of uniserial modules over a valuation domain
• Groups in the class semigroup of a prüfer domain of finite character
• t-class semigroups of integral domains
• The Topology of Ordered Abelian Groups
• Clifford regular domains

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