Some Types of Ideals in QI-Algebras

In this chapter, ideals of QI-algebra are considered. Given a subset of a right distributive QI-algebra, the smallest ideal containing it is constructed. Also, the notions of implicative ideal, fantastic ideal, and normal ideal in a right distributive QI-algebra are introduced, and the authors proved that these notions are equivalent.

Relations of the Algebra of Polynomial Integrodifferential Operators

We revisit the algebra of polynomial integrodifferential operators and we give a generalization of its relations. Generators of prime ideals of height 1, of the maximal ideal, and of the smallest ideal of In are discussed. A technique for obtaining a generating set for a given two-sided ideal of In is also discussed.

On Extensions of Stably FiniteC*-Algebras (II)

For any C*-algebra A with an approximate unit of projections, there is a smallest ideal I of A such that the quotient A/I is stably finite. In this paper a sufficient and necessary condition for an ideal of a C*-algebra with real rank zero to be this smallest ideal is obtained by using K-theory

On Ideals of Implication Groupoids

Ideals of implication groupoids are considered. Given a subset of a distributive implication groupoid, the smallest ideal containing it is constructed. A characterization of ideals in distributive implication groupoid using upper sets is given.

Separating Points of βℕ By Minimal Flows

We consider minimal left ideals L of the universal semigroup compactification of a topological semigroup S. We show that the enveloping semigroup of L is homeomorphically isomorphic to if and only if given q ≠ r in , there is some p in the smallest ideal of with qp ≠ rp. We derive several conditions, some involving minimal flows, which are equivalent to the ability to separate q and r in this fashion, and then specialize to the case that S = , and the compactification is . Included is the statement that some set A whose characteristic function is uniformly recurrent has .