Semiring and Semimodule Issues in MV-Algebras

DOI10.1080/00927872.2011.610074zbMath1317.06012arXiv1002.4013OpenAlexW2115792424MaRDI QIDQ2839091

Ciro Russo, Antonio Di Nola

Publication date: 4 July 2013

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

Full work available at URL: https://arxiv.org/abs/1002.4013

zbMATH Keywords

MV-algebrasidempotent semiringssemimodules

Mathematics Subject Classification ID

MV-algebras (06D35) Semirings (16Y60) Many-valued logic (03B50)

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The zero-divisor graphs of MV-algebras ⋮ Corrigendum to “Semiring and semimodule issues in MV-algebras, Communications in Algebra 41:3 (2013), 1017–1048” ⋮ Tropical linear algebra with the Łukasiewicz t-norm ⋮ Injective and projective semimodules over involutive semirings ⋮ Cayley's and Holland's theorems for idempotent semirings and their applications to residuated lattices ⋮ Module Structure on Effect Algebras ⋮ Annihilator graphs of MV-algebras ⋮ Structure and representation of semimodules over inclines ⋮ Steady states in the scheduling of discrete-time systems ⋮ The semiring-theoretic approach to MV-algebras: a survey ⋮ Ultramatricial algebras over commutative chain semirings and application to MV-algebras ⋮ On injectivity of semimodules over additively idempotent division semirings and chain MV-semirings ⋮ An alternative construction of graphs by associating with algorithmic approach on MV-algebras

Cites Work

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• Łukasiewicz transform and its application to compression and reconstruction of digital images
• Interpretation of AF \(C^*\)-algebras in Łukasiewicz sentential calculus
• Tensor product of functors
• Duality and separation theorems in idempotent semimodules.
• Tensor products of idempotent semimodules. An algebraic approach
• Algebraic foundations of many-valued reasoning
• Toward homological characterization of semirings: Serre's conjecture and Bass's perfectness in a semiring context.
• On flat semimodules over semirings.
• Onp-Schreier Varieties of Semimodules
• MORITA EQUIVALENCE AND HOMOLOGICAL CHARACTERIZATION OF SEMIRINGS
• Commutative rings whose ideals form an MV-algebra
• A Unified Algebraic Framework for Fuzzy Image Compression and Mathematical Morphology
• A constructive proof of McNaughton's theorem in infinite-valued logic
• A geometric proof of the completeness of the Łukasiewicz calculus
• Idempotent structures in optimization