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Sibirsk. Mat. Zh., 2011, Volume 52, Number 6, Pages 1329–1340 (Mi smj2277)  

Categorical Horn theories and modules

E. A. Palyutinab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University, Novosibirsk

Abstract: We study connection between categorical Horn theories and modules. We show that each function enrichment of any abelian group to a primitive normal structure is primitively equivalent to some module. We give a description for the categorical Horn classes of modules. We propose some sufficient conditions for a categorical Horn theory to be primitively equivalent to a theory of modules. In particular, such are the categorical Horn theories of enrichments of abelian groups with the conditions of primitive rank $\le3$ and the absence of predicate symbols of arity $\ge3$ in the language.

Keywords: categorical theory, Horn class, module, primitive formula, normal formula.

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English version:
Siberian Mathematical Journal, 2011, 52:6, 1056–1064

Bibliographic databases:

UDC: 510.67+512.57
Received: 17.05.2011

Citation: E. A. Palyutin, “Categorical Horn theories and modules”, Sibirsk. Mat. Zh., 52:6 (2011), 1329–1340; Siberian Math. J., 52:6 (2011), 1056–1064

Citation in format AMSBIB
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\paper Categorical Horn theories and modules
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\vol 52
\issue 6
\pages 1329--1340
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\jour Siberian Math. J.
\yr 2011
\vol 52
\issue 6
\pages 1056--1064
\crossref{https://doi.org/10.1134/S0037446611060103}
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