Groups in the class semigroups of valuation domains

DOI10.1007/BF02761037zbMath0869.13006OpenAlexW2094924792WikidataQ105710967 ScholiaQ105710967MaRDI QIDQ1817272

Silvana Bazzoni, Luigi Salce

Publication date: 6 February 1997

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02761037

zbMATH Keywords

valuation domainclass semigroupfractional ideals

Mathematics Subject Classification ID

Valuation rings (13F30) Torsion-free groups, infinite rank (20K20) Class groups (13C20)

Related Items (21)

Groups in the class semigroup of a prüfer domain of finite character ⋮ Ideal class semigroups of overrings ⋮ Ideal semigroups of noetherian domains and Ponizovski decompositions ⋮ Integral domains with Boolean \(t\)-class semigroup ⋮ Ten Problems on Stability of Domains ⋮ On the class semigroup of \(\mathbb{Z}_S\)-fields and Iwasawa invariants ⋮ Class semigroups of integral domains ⋮ Structure of general ideal semigroups of monoids and domains ⋮ The class semigroup of local one-dimensional domains ⋮ Star stability and star regularity for Mori domains ⋮ On the class semigroup of the cyclotomic \(\mathbb Z_p\)-extension of the rational numbers ⋮ Clifford regular domains ⋮ Finite character, local stability property and local invertibility property ⋮ Graded Prüfer domains with Clifford homogeneous class semigroups ⋮ t-class semigroups of integral domains ⋮ Constituent groups of Clifford semigroups arising from \(t\)-closure ⋮ Clifford semigroups of ideals in monoids and domains ⋮ On infinite extensions of Dedekind domains, upper semicontinuous functions and the ideal class semigroups ⋮ w-Stability and Cliffordw-Regularity of Polynomial Rings ⋮ Ideal theory in Prüfer domains -- an unconventional approach ⋮ Stability and Clifford Regularity with Respect to Star Operations

Cites Work

• On the algebraic compactness of some quotients of product groups
• Induktive Limiten endlich erzeugter freier Moduln
• Verallgemeinerung eines Satzes von Herrn F. Specker
• Abelian groups that are direct summands of every abelian group which contains them as pure subgroups
• The class semigroup of orders in number fields
• The hierarchy of uniserial modules over a valuation domain
• The structure of the factor group of the unrestricted sum by the restricted sum of Abelian groups II
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