Commutative subalgebras from Serre relations

FUZZY CONVEX SUBALGEBRAS OF COMMUTATIVE RESIDUATED LATTICES

In this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. In particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. Then we study fuzzy...

Dcpos of Commutative C*-subalgebras

Serre Finiteness and Serre Vanishing for Non-commutative P-bundles

Suppose X is a smooth projective scheme of finite type over a field K, E is a locally free OX -bimodule of rank 2, A is the non-commutative symmetric algebra generated by E and ProjA is the corresponding non-commutative P -bundle. We use the properties of the internal Hom functor HomGrA(−,−) to prove versions of Serre finiteness and Serre vanishing for ProjA. As a corollary to Serre finiteness,...

Serre Duality for Non-commutative P-bundles

Abstract. Let X be a smooth scheme of finite type over a field K, let E be a locally free OX -bimodule of rank n, and let A be the non-commutative symmetric algebra generated by E. We construct an internal Hom functor, HomGrA(−,−), on the category of graded right A-modules. When E has rank 2, we prove that A is Gorenstein by computing the right derived functors of HomGrA(OX ,−). When X is a smo...

Commutative subalgebras of the Grassmann algebra

The maximal dimension of a commutative subalgebra of the Grassmann algebra is determined. It is shown that for any commutative subalgebra there exists an equidimensional commutative subalgebra spanned by monomials. It follows that the maximal dimension of a commutative subalgebra can be expressed in terms of the maximal size of an intersecting system of subsets of odd size in a finite set. 2010...