Free modules with two distinguished submodules

DOI10.1080/00927879708826063zbMath0887.16014OpenAlexW2083329590MaRDI QIDQ4361013

Rüdiger Göbel, Manfred Dugas, Warren May

Publication date: 10 March 1998

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

Full work available at URL: https://doi.org/10.1080/00927879708826063

zbMATH Keywords

free modulespartially ordered setsButler groupsendomorphism algebrascategories of representationsmodules with distinguished submodules

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Representations of quivers and partially ordered sets (16G20) Structure, classification theorems for modules and ideals in commutative rings (13C05) Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30) Direct sums, direct products, etc. for abelian groups (20K25) Torsion-free groups, finite rank (20K15)

Related Items (6)

Endomorphism rings of \(B_2\)-groups of infinite rank ⋮ Remarks about the history of Abelian groups in England and Germany. ⋮ Endomorphism algebras of peak $I$-spaces over posets of infinite prinjective type ⋮ Representations over PID’s with three distinguished submodules ⋮ Classification of modules with two distinguished pure submodules and bounded quotients ⋮ Does the automorphism group generate the endomorphism ring in \(\text{Rep}(S,R)\)?

Cites Work

• Four submodules suffice for realizing algebras over commutative rings
• Tame algebras and integral quadratic forms
• Every cotorsion-free algebra is an endomorphism algebra
• Endomorphism algebras of modules with distinguished partially ordered submodules over commutative rings
• Infinite Abelian groups, Whitehead problem and some constructions
• Automorphism groups of fields
• Endomorphism algebras of large modules with distinguished submodules
• Countable Butler groups and vector spaces with four distinguished subspaces
• Independence in Completions and Endomorphism Algebras
• Prescribing Endomorphism Algebras, a Unified Treatment
• Butler groups with finite typesets and free groups with distinguished subgroups
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