Cancellation over commutative rings of dimension one and two

DOI10.1016/0021-8693(84)90077-2zbMath0539.13006OpenAlexW2049979329MaRDI QIDQ793790

Roger Wiegand

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1016/0021-8693(84)90077-2

zbMATH Keywords

quadratic orderintegral group ringsNoetherian ringquadratic orderscoordinate ring of a singular affine curvedirect sum cancellationregular integral domaintorsionfree cancellation

Mathematics Subject Classification ID

Group rings (16S34) Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Quadratic extensions (11R11) Commutative Noetherian rings and modules (13E05) Integral domains (13G05) Structure, classification theorems for modules and ideals in commutative rings (13C05) Relevant commutative algebra (14A05)

Related Items

Lattices over Bass rings and graph agglomerations, Cancellation of finite-dimensional Noetherian modules, Picard groups of singular affine curves over a perfect field, Direct sum behavior of lattices over sigma-I rings, Ranks of indecomposable modules over one-dimensional rings, Matrix zeros of quadratic equations, Torsionfree modules over one-dimensional Noetherian rings, Direct-sum cancellation for modules over real quadratic orders, Direct-sum cancellation: Modules versus lattices¹, Irreducible maps of commutative rings, Ideal classes of orders in quaternion algebras, Finite representation type and direct-sum cancellation., Strongly two-generated ideals, Locally tame plane polynomial automorphisms, Cancellation and direct summands in dimension 1, Criteria for direct-sum cancellation, with an application to negative quadratic orders, Direct sum cancellation for modules over one-dimensional rings, PROJECTIVE PRESENTATIONS OF FINITELY GENERATED MODULES WITH LARGE ANNIHILATORS, FAILURE OF CANCELLATION FOR QUARTIC AND HIGHER-DEGREE ORDERS, Unique decompositions into ideals for noetherian domains., Power cancellation for artinian modules, A mixed version for a Fuchs' lemma, Some $K$-theoretic properties of the kernel of a locally nilpotent derivation on $k[X_1, \dots , X_4$], Stable isomorphism of modules over one-dimensional rings, Dedekind-like behavior of rings with 2-generated ideals, Presentations over HNP rings with enough invertible ideals and torsionfree cancellation over neoclassical orders, On the krull-schmidt-azumaya theorem for integral group rings, Torsion-free modules over reduced Witt rings, Modules over Dedekind-like rings, Rings with two-generated ideals, Cancellation of hyperbolic ε-hermitian forms and of simple knots, Picard groups and torsion-free cancellation for orders in \(\mathbb Z \times \mathbb Z \times \mathbb Z\)

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