Categorical Horn theories and modules

E. A. Palyutin<sup>ab

a</sup> 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.

UDC: 510.67+512.57

Received: 17.05.2011

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

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