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Injectives and Projectives in Term Finite Varieties of Algebras

Published online by Cambridge University Press:  20 November 2018

George F. McNulty ,
T. Nordahl  and
H. E. Scheiblich
George F. McNulty
Affiliation:
University of South Carolina, Columbia, South Carolina
T. Nordahl
Affiliation:
Medical University of South Carolina, Charleston, South Carolina
H. E. Scheiblich
Affiliation:
Medical University of South Carolina, Charleston, South Carolina
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Let V be a class of similar algebras. An algebra is V-injective provided and whenever and fis a one-to-one homomorphism from into and g is a homomorphism from into , then there is a homomorphism h from into such that h º f = g. So is injective provided all diagrams of the following sort can be completed.

Dually, is V-projective provided and whenever and f is a homomorphism from onto and g is a homomorphism from into , then there is a homomorphism h from into such that f º h = g. So is projective provided all diagrams of the following sort can be completed:

This usage of the words “projective” and “injective” differs somewhat from the usage current in category theory.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 35 , Issue 5 , 01 October 1983 , pp. 769 - 775
Copyright
Copyright © Canadian Mathematical Society 1983

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