Abelian groups and representations of finite partially ordered sets

Publication date: 13 August 2000

Published in: CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC (Search for Journal in Brave)

zbMATH Keywords

endomorphism rings quasi-isomorphisms almost completely decomposable groups finite representation type tame representation type typesets wild representation type pure subgroups almost split sequences indecomposable representations category equivalences finite partially ordered sets representations of posets torsion-free Abelian groups of finite rank quasi-homomorphisms bracket groups categories of Butler groups direct sums of rank-1 groups near isomorphisms

Mathematics Subject Classification ID

Representation type (finite, tame, wild, etc.) of associative algebras (16G60) Representations of quivers and partially ordered sets (16G20) Homological and categorical methods for abelian groups (20K40) Direct sums, direct products, etc. for abelian groups (20K25) Torsion-free groups, finite rank (20K15) Research exposition (monographs, survey articles) pertaining to group theory (20-02) Research exposition (monographs, survey articles) pertaining to associative rings and algebras (16-02)

Related Items (53)

Submodule categories of wild representation type. ⋮ Localizations of torsion-free Abelian groups. ⋮ Gorenstein projective bimodules via monomorphism categories and filtration categories ⋮ Representations of finite partially ordered sets over commutative Artinian uniserial rings. ⋮ Prinjective Ringel-Hall algebras for posets of finite prinjective type. ⋮ Quasi-e-locally cyclic torsion-free abelian groups ⋮ Tensor products and endomorphism rings of finite valuated groups ⋮ Pure subgroups of completely decomposable groups and a group class problem. ⋮ Unnamed Item ⋮ Monomorphism categories associated with symmetric groups and parity in finite groups. ⋮ Representation types of the category of subprojective representations of a finite poset over $K[t/(t^m)$ and a solution of a Birkhoff type problem.] ⋮ Endomorphism category of an abelian category ⋮ On the apparatus of differentiation DI-DV for posets ⋮ Monic modules and semi-Gorenstein-projective modules ⋮ The class of $(1,3)$-groups with homocyclic regulator quotient of exponent $p^4$ has bounded representation type. ⋮ The classification problem for $S$-local torsion-free abelian groups of finite rank ⋮ Algebraically equipped posets ⋮ Almost completely decomposable groups and unbounded representation type. ⋮ Nilpotent category of monoidal category and tensor-hom adjunction ⋮ On vector spaces with distinguished subspaces and redundant base. ⋮ Remarks about the history of Abelian groups in England and Germany. ⋮ Completely decomposable Abelian groups with a distinguished cd subgroup. ⋮ Sharp types revisited. ⋮ Commutative endomorphism algebras of torsion-free, rank-two Kronecker modules with singular height functions. ⋮ Chain categories of modules and subprojective representations of posets over uniserial algebras. ⋮ Adjoint functors, projectivization, and differentiation algorithms for representations of partially ordered sets. ⋮ Unnamed Item ⋮ Torsion-free modules of finite rank over a discrete valuation ring. ⋮ A geometric realization of socle-projective categories for posets of type $\mathbb{A}$ ⋮ Duality for almost completely decomposable groups. ⋮ Monomorphism categories, cotilting theory, and Gorenstein-projective modules. ⋮ A Remak-Krull-Schmidt Class of Torsion-Free Abelian Groups ⋮ A condition of indecomposability for Butler $\mathrm B(n)$-groups. ⋮ Modules over discrete valuation domains. III ⋮ Modules over discrete valuation domains. I ⋮ Representation-finite Birkhoff type problems for nilpotent linear operators ⋮ Settings for a study of finite rank Butler groups. ⋮ A specialization of prinjective Ringel-Hall algebra and the associated Lie algebra. ⋮ $(1,2)$-groups with $p^3$-regulator quotient. ⋮ Pure $B(n)$-subgroups of completely decomposable groups. ⋮ Direct sums of local torsion-free abelian groups ⋮ Generalized almost completely decomposable groups. ⋮ Tame-wild dichotomy of Birkhoff type problems for nilpotent linear operators. ⋮ Modules over discrete valuation domains. II ⋮ Conductor of an Abelian group. ⋮ Valuated Butler groups of finite rank ⋮ On endomorphism rings of $B_1$-groups that are not $B_2$-groups ⋮ The existence of Hall polynomials for $x^2$-bounded invariant subspaces of nilpotent linear operators ⋮ On Corner type endo-wild algebras. ⋮ Bounded submodules of modules. ⋮ Pi-balanced torsion-free modules over a discrete valuation domain ⋮ Indecomposable (1,3)-Groups and a matrix problem ⋮ An endomorphism algebra realization problem and Kronecker embeddings for algebras of infinite representation type

This page was built for publication: Abelian groups and representations of finite partially ordered sets