Commutative ideal theory without finiteness conditions: Completely irreducible ideals

DOI10.1090/S0002-9947-06-03815-3zbMath1091.13011OpenAlexW1620498138MaRDI QIDQ3378466

Bruce Olberding, László Fuchs, William J. Heinzer

Publication date: 3 April 2006

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-06-03815-3

zbMATH Keywords

arithmetical ringcompletely irreducible idealcomplete intersection lattice ideals

Mathematics Subject Classification ID

Ideal theory for semigroups (20M12) Linkage, complete intersections and determinantal ideals (13C40) Polynomial rings and ideals; rings of integer-valued polynomials (13F20)

Related Items (18)

Distinguished classes of ideal spaces and their topological properties ⋮ Generalizations of strongly hollow ideals and a corresponding topology ⋮ Products and intersections of prime-power ideals in Leavitt path algebras ⋮ The Multiplicative Ideal Theory of Leavitt Path Algebras of Directed Graphs—A Survey ⋮ Arithmetical rings ⋮ The multiplicative ideal theory of Leavitt path algebras ⋮ Unique irredundant intersections of completely irreducible ideals ⋮ Some Properties of Completely Arithmetical Rings ⋮ The ideal theory of intersections of prime divisors dominating a normal Noetherian local domain of dimension two ⋮ Irreducibility in the Total Ring of Quotients ⋮ Strongly Irreducible Ideals and Truncated Valuations ⋮ The Dual Notions of Some Generalizations of Prime Submodules ⋮ Homomorphic images of subdirectly irreducible rings ⋮ Trivial extensions defined by Prüfer conditions ⋮ Zariski Topologies for Coprime and Second Submodules ⋮ On \(S\)-second spectrum of a module ⋮ A note on the Dixmier-Moeglin equivalence in Leavitt path algebras of arbitrary graphs over a field ⋮ Completely Arithmetical Rings

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