On the foundations of inverse monoids and inverse algebras

DOI10.1017/S0013091500019398zbMath0891.16017OpenAlexW1972641171MaRDI QIDQ4354305

Pedro A. Guil Asensio, José L. Gómez Pardo

Publication date: 16 September 1997

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0013091500019398

zbMATH Keywords

direct summandsGoldie dimensionCS-modulesfinite-dimensional modulesdirect sums of uniform modulesfinitely generated quasi-continuous modules

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Homological dimension in associative algebras (16E10) Chain conditions on annihilators and summands: Goldie-type conditions (16P60)

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On the Goldie dimension of rings and modules., Every Σ-CS-module has an indecomposable decomposition, Hereditary rings with countably generated cotorsion envelope.

Cites Work

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• The \({\mathcal D}\)-category of a monoid
• Constructing inverse monoids from small categories
• The geometric theory of inverse semigroups. I: E-unitary inverse semigroups
• Inverse Monoids With a Natural Semilattice Ordering