Combinatorial dimensions: Indecomposability on certain local finite-dimensional trivial extension algebras

DOI10.1142/S0219498814500248zbMath1294.05106arXiv1308.4709OpenAlexW2114574777MaRDI QIDQ5420693

Juan Orendain

Publication date: 13 June 2014

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.4709

zbMATH Keywords

dimensionmoduleindecomposable graph

Mathematics Subject Classification ID

Applications of graph theory (05C90) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Commutative Noetherian rings and modules (13E05) Commutative Artinian rings and modules, finite-dimensional algebras (13E10) Connectivity (05C40) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15) Local rings and semilocal rings (13H99) Commutative ring extensions and related topics (13B99) Associative rings and algebras arising under various constructions (16S99) Finite commutative rings (13M99)

Cites Work

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• Module theory. Endomorphism rings and direct sum decompositions in some classes of modules
• On a directly indecomposable abelian group of power greater than continuum
• The existence of indecomposable abelian groups of arbitrary power
• Corrections and Supplementaries to My Paper concerning Krull-Remak-Schmidt’s Theorem
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