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lattice filter

Defines: 
filter, prime filter, ultrafilter, filter generated by, principal filter
Synonym: 
ultra filter, ultra-filter, maximal filter
Type of Math Object: 
Definition
Major Section: 
Reference
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Mathematics Subject Classification

06B10 no label found

Comments

I am not sure, but I think to define filter of lattices. One does assume that the Lattice has a least element. Although, I do not see why this is necessary.

What do you mean filter of lattices? Or do you mean filter of a lattice? Given a lattice or more generally a poset, a filter can be defined without the lattice (or poset) having a least element.

This is how Lambek has defined it in his book "Lectures on Rings and Modules" .. he had a special reason for doing so, but Im rather shaggy today .. Im sure though that the definition with least element became necessary later on in his book.

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