On Serre's Problem on Projective Semimodules over Polynomial Semirings

DOI10.1080/00927872.2013.804529zbMath1306.16044OpenAlexW2063724823MaRDI QIDQ2876262

S. N. Il'in, Yefim Katsov

Publication date: 18 August 2014

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

Full work available at URL: https://doi.org/10.1080/00927872.2013.804529

zbMATH Keywords

projective semimodulesfree semimodulesdivision semiringscategories of semimodulespolynomial semirings\(\mathbb N\)-valued semirings\(p\)-Schreier varieties

Mathematics Subject Classification ID

Free, projective, and flat modules and ideals in associative algebras (16D40) Projectives and injectives (category-theoretic aspects) (18G05) Semirings (16Y60) Free algebras (08B20) (T)-ideals, identities, varieties of associative rings and algebras (16R10) Injectives, projectives (08B30)

Related Items (5)

On congruence-semisimple semirings and the \(K_{0}\)-group characterization of ultramatricial algebras over semifields ⋮ PROJECTIVE AND INJECTIVE PARTIAL MODULES AND UNIVERSAL APPLICATIONS ⋮ On the homological classification of semirings ⋮ Ultramatricial algebras over commutative chain semirings and application to MV-algebras ⋮ On injectivity of semimodules over additively idempotent division semirings and chain MV-semirings

Cites Work

• Projective modules over group rings
• On the ranks of idempotent matrices over skew semifields
• On the applicability to semirings of two theorems from the theory of rings and modules.
• Cancellation of Azumaya algebras
• Toward homological characterization of semirings: Serre's conjecture and Bass's perfectness in a semiring context.
• Projective semimodules over semirings with valuations in nonnegative integers.
• Onp-Schreier Varieties of Semimodules
• On semimodules over commutative, additively idempotent semirings

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