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Atomicity And Nilpotence

Published online by Cambridge University Press:  20 November 2018

Keith A. Kearnes
Keith A. Kearnes*
Affiliation:
University of Hawaii at Manoa, Honolulu, Hawaii
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There is a body of results for lattices known as “Decomposition Theory” which is aimed at proving certain existence and uniqueness theorems concerning irredundant representations of elements of a compactly generated lattice. The motivation for these results is certainly the quest for sufficient conditions on congruence lattices to insure irredundant subdirect representations of algebras. These theorems usually include some kind of modularity or distribut i v e hypothesis (for uniqueness) and some atomicity hypothesis (for existence); the precise details can be found in [3]. The atomicity condition is usually the hypothesis that the lattice in question is strongly atomic or at least atomic. Now, it is well-known that every algebra has a weakly atomic congruence lattice.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 2 , 01 April 1990 , pp. 365 - 382
Copyright
Copyright © Canadian Mathematical Society 1990

References

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