Algebraically flat or projective algebras

K-FLAT PROJECTIVE FUZZY QUANTALES

In this paper, we introduce the notion of {bf K}-flat projective fuzzy quantales, and give an elementary characterization in terms of a fuzzy binary relation on the fuzzy quantale. Moreover, we  prove that {bf K}-flat projective fuzzy quantales are precisely the coalgebras for a certain comonad on the category of fuzzy quantales. Finally, we present two special cases of {bf K} as examples.

Projective Planes in Algebraically

We investigate the combinatorial geometry obtained from algebraic closure over a fixed subfield in an algebraically closed field. The main result classifies the subgeometries which are isomorphic to projective planes. This is applied to give new examples of algebraic characteristic sets of matroids. The main technique used, which is motivated by classical projective geometry, is that a particul...

Flat Projective Connections

Noetherian algebras over algebraically closed fields

Let k be an uncountable algebraically closed field and let A be a countably generated left Noetherian k-algebra. Then we show that A⊗k K is left Noetherian for any field extension K of k. We conclude that all subfields of the quotient division algebra of a countably generated left Noetherian domain over k are finitely generated extensions of k. We give examples which show that A⊗k K need not re...

Algebraically Expandable Classes of Implication Algebras

In this work we solve the following problem: Characterize the subclasses of implication algebras that can be axiomatized by sentences of the form 89! ^ p = q. In the process we obtain a representation result for …nite implication algebras, and as a by-product of our solution a number of interesting classes of implication algebras arise. We also obtain a characterization of the congruence permut...