Remarks on theories of free algebras and modules

arXiv2004.10351MaRDI QIDQ6339188

Publication date: 21 April 2020

Abstract: We ask some questions and make some observations about the (complete) theory T (infinity, V) of free algebras in V on infinitely many generators, where V is a variety in the sense of universal algebra. We focus on the case T(infinity, R) where V is the variety of R-modules (R a ring). Building on work in Kucera-Pillay we characterize when all models of T(infinity, R) are free, projective, flat, as well as when T(infinity,R) is categorical in a higher power.

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Free, projective, and flat modules and ideals in associative algebras (16D40) Classification theory, stability, and related concepts in model theory (03C45) Equational classes, universal algebra in model theory (03C05)

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