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Fall 1996 Higman's Embedding Theorem in a General Setting and Its Application to Existentially Closed Algebras
Oleg V. Belegradek
Notre Dame J. Formal Logic 37(4): 613-624 (Fall 1996). DOI: 10.1305/ndjfl/1040046145

Abstract

For a quasi variety of algebras K, the Higman Theorem is said to be true if every recursively presented K-algebra is embeddable into a finitely presented K-algebra; the Generalized Higman Theorem is said to be true if any K-algebra which is recursively presented over its finitely generated subalgebra is embeddable into a K-algebra which is finitely presented over this subalgebra. We suggest certain general conditions on K under which (1) the Higman Theorem implies the Generalized Higman Theorem; (2) a finitely generated K-algebra A is embeddable into every existentially closed K-algebra containing a finitely generated K-algebra B if and only if the word problem for A is Q-reducible to the word problem for B. The quasi varieties of groups, torsion-free groups, and semigroups satisfy these conditions.

Citation

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Oleg V. Belegradek. "Higman's Embedding Theorem in a General Setting and Its Application to Existentially Closed Algebras." Notre Dame J. Formal Logic 37 (4) 613 - 624, Fall 1996. https://doi.org/10.1305/ndjfl/1040046145

Information

Published: Fall 1996
First available in Project Euclid: 16 December 2002

zbMATH: 0882.03036
MathSciNet: MR1446232
Digital Object Identifier: 10.1305/ndjfl/1040046145

Subjects:
Primary: 03D45
Secondary: 03C60, 03D40, 08C15, 20F10

Rights: Copyright © 1996 University of Notre Dame

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Vol.37 • No. 4 • Fall 1996
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