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Injectives and Projectives in Term Finite Varieties of Algebras

  • George F. McNulty (a1), T. Nordahl (a2) and H. E. Scheiblich (a2)

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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.

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References

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Injectives and Projectives in Term Finite Varieties of Algebras

  • George F. McNulty (a1), T. Nordahl (a2) and H. E. Scheiblich (a2)

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