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Formations, bihomorphisms and natural transformations

Published online by Cambridge University Press:  17 April 2009

Andrew Ensor
Andrew Ensor
Affiliation:
Dipartimento di Matematica, Università di Siena, Via del Capitano 15, 53100 Siena, Italia. e-mail: ensor@unisi.it
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Abstract

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Given a variety ν and ν-algebras A and B, an algebraic formationF: A ⇉ B is a ν-homomorphism FL R × A → B, for some ν-algebra R, and the resulting functions F (r,-): A → B for r ∈ R are termed formable. Firstly, as motivation for the study of algebraic formations, categorical formations and their relationship with natural transformations are explained. Then, formations and formable functions are described for some common varieties of algebras, including semilattices, lattices, groups, and implication algebras. Some of their general properties are investigated for congruence modular varieties, including the description of a uniform congruence which provides information on the structure of B.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 2 , April 2000 , pp. 217 - 239
Copyright
Copyright © Australian Mathematical Society 2000

References

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