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A note on some types of filters in MTL-algebras

✍ Scribed by Haveshki, Masoud

Book ID
121829196
Publisher
Elsevier Science
Year
2014
Tongue
English
Weight
183 KB
Volume
247
Category
Article
ISSN
0165-0114

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We show that for every uncountable regular K and every K-complete Boolean algebra B of density 5 K there is a filter F B such that the number of partitions of length < K modulo F is 5 2'". We apply this to Boolean algebras of the form P ( X ) / I , where I is a n-complete K-dense ideal on X .

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A denotes an artin algebra in the sense of Auslander, i.e., an associative algebra of finite length over a commutative artinian ring Z. We assume in addition that Z is local and that its residue field k is algebraically closed, whence infinite. As a partial answer to a w x question raised by Ausland