Divisibility theory in commutative rings: Bezout monoids

DOI10.1090/S0002-9947-2012-05424-9zbMath1280.06010OpenAlexW3023835097MaRDI QIDQ2841340

László Márki, Ánh, Phạm Ngọc, Peter Vámos

Publication date: 25 July 2013

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-2012-05424-9

zbMATH Keywords

spectrumBezout ringBezout monoidprime filterlattice-ordered semigroupdivisibility in ringsdivisibility semigroupsheaf representations of rings

Mathematics Subject Classification ID

Commutative semigroups (20M14) Ordered semigroups and monoids (06F05) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Divisibility and factorizations in commutative rings (13A05)

Related Items (8)

Generalization of a theorem of Clifford ⋮ Divisibility theory in commutative rings: Bézout monoids ⋮ A classification of certain group-like \(\mathrm{FL}_e\)-chains ⋮ Studying monoids is not enough to study multiplicative properties of rings: an elementary approach. ⋮ Divisibility theory of semi-hereditary rings ⋮ Divisibility Theory of Arithmetical Rings with One Minimal Prime Ideal ⋮ Factorization theory in commutative monoids ⋮ Gauss’ lemma and valuation theory

Cites Work

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• Archimedean Prüfer structures alias filter Archimedean \(d\)-semigroups
• Some remarks on elementary divisor rings. II
• The minimal prime spectrum of a reduced ring
• Theory of \(x\)-ideals
• Abstract commutative ideal theory
• On generalized valuation rings
• Distributive modules
• Abstract commutative ideal theory without chain condition
• Ideal divisibility monoids
• Rings whose finitely generated modules are direct sums of cyclics
• Zur Theorie der Teilbarkeitshalbgruppen. (On the theory of divisibility semigroups)
• Über die Ideale arithmetischer Ringe
• Contribution à l'étude des groupes ordonnés
• Divisibility theory of semi-hereditary rings
• Rings of Continuous Functions in Which Every Finitely Generated Ideal is Principal
• Concerning bricks
• Representable divisibility semigroups
• Modules Whose Lattice of Submodules is Distributive
• Multiplication Ideals, Multiplication Rings, and the Ring R(X)
• Elementary Divisor Rings and Finitely Presented Modules
• A Remark on Arithmetical Rings
• Arithmetical rings
• Modules over commutative regular rings
• Semi-Valuations and Groups of Divisibility
• Darstellung von Halbgruppen und universellen Algebren durch Schnitte in Garben; bireguläre Halbgruppen
• Komplementäre Halbgruppen. Axiomatik und Arithmetik
• Applications of the Theory of Boolean Rings to General Topology
• Residuated Lattices
• Elementary Divisors and Modules
• Naturally Totally Ordered Commutative Semigroups

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