Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-25T05:01:26.609Z Has data issue: false hasContentIssue false

Formations, bihomorphisms and natural transformations

Published online by Cambridge University Press:  17 April 2009

Andrew Ensor
Affiliation:
Dipartimento di Matematica, Università di Siena, Via del Capitano 15, 53100 Siena, Italia. e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Given a variety ν and ν-algebras A and B, an algebraic formationF: AB is a ν-homomorphism FL R × AB, for some ν-algebra R, and the resulting functions F (r,-): AB for rR 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
Copyright
Copyright © Australian Mathematical Society 2000

References

REFERENCES

[1]Ensor, A., ‘Algebraic coalitions’, Algebra Universalis 38 (1997), 114.CrossRefGoogle Scholar
[2]Ensor, A., ‘Templates and worlds for representing mathematical notions’, (preprint).Google Scholar
[3]Freese, R. and McKenzie, R., Commutarot theory for congruence modular varieties, London Mathematical Society Lecture Note Series 125 (Cambrige University Press, Cambridge, New York, 1987).Google Scholar
[4]Gumm, H.P., ‘Congruence modularity is permutability composed with distributivity’, Arch. Math. 36 (1981), 569576.Google Scholar
[5]Hermann, C., ‘Affine algebras in congruence-modular varieties’, Acta Sci. Math. (Szeged) 41 (1979), 119125.Google Scholar
[6]MacLane, S., Categories for the working mathematician (Springer-Verlag, Berlin, Heidelberg, New York, 1971).Google Scholar
[7]Rasiowa, H., An algebraic approach to non-classical logics, Studies in Logic and the Foundations of Mathematics (North-Holland Publishing Co. Inc., Amsterdam, London, 1974).Google Scholar