Module equivalences: Local to global. When primitive polynomials represent units

DOI10.1016/0021-8693(82)90282-4zbMath0492.13005OpenAlexW2055265077MaRDI QIDQ1167766

Robert M. Guralnick, Dennis R. Estes

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1016/0021-8693(82)90282-4

zbMATH Keywords

von Neumann regular ringslocal-global principleDedekindring of algebraic integersLG ringpolynomials representing units

Mathematics Subject Classification ID

Polynomials over commutative rings (13B25) Commutative rings and modules of finite generation or presentation; number of generators (13E15) Extension theory of commutative rings (13B02) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items

On Transversality for Quadratic Spaces Over Rings with Many Units, Albert algebras over and other rings, On rigid rings, Pole assignability in polynomial rings, power series rings, and Prüfer domains, On the orthogonal group over an LG-ring, The genus of a module. II: Roiter's theorem, power cancellation and extension of scalars, Absolute stable rank and Witt cancellation for noncommutative rings, Similarity of holomorphic matrices, Pole assignability and the invariant factor theorem in Prüfer domains and Dedekind domains, A stable range for quadratic forms over commutative rings, Polynomial rings which are BCS rings, Extensions cubiques à base normale. (Cubic extensions with normal basis), The Krull-Schmidt property for ideals and modules over integral domains., On the primitive element and normal basis theorems, Pseudosimilarity and cancellation of modules, Matrix equivalence and isomorphism of modules, Direct-sum cancellation of submodule systems, Similarity of matrices over commutative rings, Cancellation and direct summands in dimension 1, Local to global equivalence for homomorphisms, Strong feedback cyclization for systems over rings, Dynamic feedback over rings whose homomorphic images are local-global, Finitely Presented Modules Over Semihereditary Rings, Krull-Schmidt Fails for Artinian Modules, Stability in Commutative Rings, The primitive topology of a scheme, Locally isomorphic torsionless modules over domains of finite character, Witt rings of LG-rings, Unnamed Item, Equivalent generating vectors of finitely generated modules over commutative rings, The genus of a module, On diophantine equations over the ring of all algebraic integers, Indecomposable Modules and Gelfand Rings, Representations under ring extensions: Latimer-MacDuffee and Taussky correspondences, Hypersurfaces in projective schemes and a moving lemma

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