The Algebra of Filters of a Cubic Algebra

Details The Algebra of Filters of a Cubic Algebra The Algebra of Filters of a Cubic Algebra

2009-01-30

arxiv.org/abs/0901.4933v1

Mathematics

Rings and Algebras

22 pages, ams-latex

Scientific paper

In this paper we discuss the inclusion ordering on the filters of a filter algebra, a special type of Metropolis-Rota algeba. Using embeddings into interval algebras we show that the notion of "untwisted" gives rise to a congruence relation on the group of g-filters. We also show that there is a natural reflection operator on the class of filters with an easily definable enveloping cubic subalgebra.

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