An Artin problem for division ring extensions and the pure semisimplicity conjecture. II

DOI10.1006/jabr.1999.8245zbMath0953.16012OpenAlexW1971544562WikidataQ122905538 ScholiaQ122905538MaRDI QIDQ1569820

Daniel Simson

Publication date: 21 January 2001

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

Full work available at URL: https://doi.org/10.1006/jabr.1999.8245

zbMATH Keywords

finite representation typedivision ringsmodule categorieshereditary ringstriangular matrix ringsdirect sums of finitely generated modulespure semisimplicity conjecture

Mathematics Subject Classification ID

Representation type (finite, tame, wild, etc.) of associative algebras (16G60) Infinite-dimensional and general division rings (16K40) Representations of associative Artinian rings (16G10) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60)

Related Items (22)

DIRECT SUM DECOMPOSITION OF THE PRODUCT OF PREINJECTIVE MODULES OVER RIGHT PURE SEMISIMPLE HEREDITARY RINGS ⋮ Endofinite modules and pure semisimple rings. ⋮ Small potential counterexamples to the pure semisimplicity conjecture ⋮ A key module over pure-semisimple hereditary rings. ⋮ Indecomposable modules over pure semisimple hereditary rings. ⋮ Superstability, Noetherian rings and pure-semisimple rings ⋮ On \(\lambda\)-pure acyclic complexes in a Grothendieck category ⋮ DEFINABLE SUBCATEGORIES OVER PURE SEMISIMPLE RINGS ⋮ Preinjective modules over pure semisimple rings. ⋮ On the endofiniteness of a key module over pure semisimple rings ⋮ On uniserial twisted group algebras of finite \(p\)-groups over a field of characteristic \(p\). ⋮ Splitting torsion pairs over pure semisimple rings. ⋮ Additive categories of locally finite representation type ⋮ Auslander-Reiten components over pure-semisimple hereditary rings. ⋮ Infinite dimensional serial algebras and their representations ⋮ Pure semisimple \(n\)-cluster tilting subcategories ⋮ Tilting cotorsion pairs and pure semisimple rings ⋮ The Gabriel-Roiter measure for right pure semisimple rings. ⋮ Coxeter Diagrams and the Köthe’s Problem ⋮ On Corner type endo-wild algebras. ⋮ PURE PROJECTIVITY AND PURE INJECTIVITY OVER FORMAL TRIANGULAR MATRIX RINGS ⋮ SOME STABLE NON-ELEMENTARY CLASSES OF MODULES

Cites Work

• Partial Coxeter functors and right pure semisimple hereditary rings
• Representations of K-species and bimodules
• Pure semisimple categories and rings of finite representation type
• A test for finite representation type
• On right pure semisimple hereditary rings and an Artin problem
• An Artin problem for division ring extensions and the pure semisimplicity conjecture. I
• The Jacobson radical power series of module categories and the representation type
• On the decomposition of modules and generalized left uniserial rings
• Quadratic Extensions of Skew Fields
• On the Sparsity of Representations of Rings of Pure Global Dimension Zero
• Strong Preinjective Partitions and Representation Type of Artinian Rings
• A characterization of hereditary rings of finite representation type
• On Rings whose Left Modules are Direct Sums of Finitely Generated Modules
• The Local Duality for Homomorphisms and an Application to Pure Semisimple PI-Rings
• Representation Theory of Artin Algebras II
• On the radical of a category
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