Four submodules suffice for realizing algebras over commutative rings

DOI10.1016/0022-4049(90)90098-3zbMath0716.16015OpenAlexW2007763357MaRDI QIDQ752813

Warren May, Rüdiger Göbel

Publication date: 1990

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(90)90098-3

zbMATH Keywords

realizationlinear endomorphisms\(K_ 4\)-module\(R_ 4\) modulecategory of R-modulesdistinguished submodulesfree A-modulefully rigid familyinfinite rank four submodules problem

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Module categories in associative algebras (16D90) Free, projective, and flat modules and ideals in associative algebras (16D40) Morphisms of commutative rings (13B10) Torsion-free groups, infinite rank (20K20) Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30)

Related Items (15)

Automorphism groups of fields ⋮ Endomorphism rings of \(B_2\)-groups of infinite rank ⋮ McLain groups over arbitrary rings and orderings ⋮ An axiomatic construction of an almost full embedding of the category of graphs into the category of \(R\)-objects ⋮ Remarks about the history of Abelian groups in England and Germany. ⋮ Free modules with two distinguished submodules ⋮ Endomorphism algebras of modules with distinguished partially ordered submodules over commutative rings ⋮ Endomorphism algebras of peak $I$-spaces over posets of infinite prinjective type ⋮ Automorphism groups of feelds.II ⋮ Representations over PID’s with three distinguished submodules ⋮ Modules with absolute endomorphism rings. ⋮ Classification of modules with two distinguished pure submodules and bounded quotients ⋮ Rigid families and endomorphism algebras of Kronecker modules ⋮ Absolutely indecomposable modules ⋮ An endomorphism algebra realization problem and Kronecker embeddings for algebras of infinite representation type

Cites Work

• Tame algebras and integral quadratic forms
• The construction of mixed modules from a theorem of linear algebra
• Large indecomposable modules in torsion theories
• Vector spaces with five distinguished subspaces
• Very decomposable Abelian groups
• Infinite Abelian groups, Whitehead problem and some constructions
• Endomorphism algebras of large modules with distinguished submodules
• Endomorphism algebras of vector spaces with distinguished sets of subspaces
• Note on extensions of Abelian groups by primary groups
• On the elementary theory of quadruples of vector spaces
• Pathological Modules over Tame Rings
• Prescribing Endomorphism Algebras, a Unified Treatment
• Endomorphism Rings of Vector Spaces and Torsion Free Abelian Groups
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