Commutative Monoids, Noncommutative Rings and Modules

DOI10.1007/978-3-030-84319-9_3OpenAlexW3206275817MaRDI QIDQ5861649

Alberto Facchini

Publication date: 1 March 2022

Published in: New Perspectives in Algebra, Topology and Categories (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-84319-9_3

zbMATH Keywords

associative ringcommutative monoidmodule over a ringpreordered abelian group

Mathematics Subject Classification ID

Ordered semigroups and monoids (06F05) Semigroups (20Mxx) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to associative rings and algebras (16-01) Modules, bimodules and ideals in associative algebras (16Dxx)

Cites Work

• Module theory. Endomorphism rings and direct sum decompositions in some classes of modules
• Pretorsion theories, stable category and preordered sets
• On the spectrum of monoids and semilattices.
• Krull Semigroups and Divisor Class Groups
• PROJECTIVE MODULES AND DIVISOR HOMOMORPHISMS
• Semilocal Categories and Modules with Semilocal Endomorphism Rings
• The Krull-Schmidt-Remak-Azumaya Theorem for 𝐺-groups
• Direct sum decompositions of modules, almost trace ideals, and pullbacks of monoids
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