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Categorical Horn theories and modules

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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 ≥ 3 and the absence of predicate symbols of arity ≤ 3 in the language.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics and Novosibirsk State University, Novosibirsk, Russia

    E. A. Palyutin

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  1. E. A. Palyutin
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Correspondence to E. A. Palyutin.

Additional information

Original Russian Text Copyright © 2011 Palyutin E. A.

The author was supported by the Russian Foundation for Basic Research (Grant 09-01-00336-a) and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-3669.2010.1).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 52, No. 6, pp. 1329–1340, November–December, 2011.

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Palyutin, E.A. Categorical Horn theories and modules. Sib Math J 52, 1056–1064 (2011). https://doi.org/10.1134/S0037446611060103

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  • DOI: https://doi.org/10.1134/S0037446611060103

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