Structure of general ideal semigroups of monoids and domains

DOI10.1216/JCA-2012-4-3-413zbMath1260.13007OpenAlexW2056937151MaRDI QIDQ1941836

Andreas Reinhart

Publication date: 22 March 2013

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

Full work available at URL: https://projecteuclid.org/euclid.jca/1361215952

zbMATH Keywords

stablesemigroupregularstar operationideal system

Mathematics Subject Classification ID

Ideal theory for semigroups (20M12) Ideals and multiplicative ideal theory in commutative rings (13A15) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (4)

The monotone catenary degree of monoids of ideals ⋮ The source of semiprimeness of semigroups ⋮ Factorization theory in commutative monoids ⋮ On the class semigroup of root-closed weakly Krull Mori monoids

Cites Work

• Star stable domains
• Ideal semigroups of noetherian domains and Ponizovski decompositions
• Constituent groups of Clifford semigroups arising from \(t\)-closure
• 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
• Clifford semigroups of ideals in monoids and domains
• The class semigroup of orders in number fields
• Groups in the class semigroup of a prüfer domain of finite character
• t-class semigroups of integral domains
• Clifford regular domains
• Localizing systems, module systems, and semistar operations
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