Birkhoff-style Theorems Through Infinitary Clone Algebras
Antonio Bucciarelli (IRIF (UMR\_8243)), Pierre-Louis Curien (IRIF, (UMR\_8243)), Arturo De Faveri (IRIF (UMR\_8243)), Antonino Salibra (IRIF, (UMR\_8243))
TL;DR
This paper extends Birkhoff's HSP theorem to the setting of infinitary algebra using clone algebras, providing a new perspective on algebraic variety representation.
Contribution
It introduces a Birkhoff-style theorem for infinitary clone algebras, broadening the classical algebraic framework to infinite operations.
Findings
Generalization of Birkhoff's theorem to infinitary algebras
Development of clone algebra framework for infinitary operations
New representation results for algebraic varieties
Abstract
Building upon the classical article "Representing varieties of algebras by algebras'' by W. D. Neumann, we revisit the famous Birkhoff's HSP theorem in the light of infinitary algebra.
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Taxonomy
TopicsAdvanced Algebra and Logic · Algebraic structures and combinatorial models · Rings, Modules, and Algebras