$M$-ideals and quasi-triangular algebras

Triangular Algebras and Ideals of Nest Algebras

Let %? be a separable Hubert space and !T c 3§(J%f) be an algebra of bounded operators. Say F is triangular if ^ n ^ * is a maximal abelian self-adjoint subalgebra (m.a.s.a.) of 3B{%?) and call this m.a.s.a. the diagonal of J7". A triangular algebra is maximal triangular if it is not properly contained in any triangular algebra. Triangular algebras of operators have been studied for 30 years no...

The Topology of Ideals in Some Triangular Af Algebras

A set of meet-irreducible ideals is described for a class of maximal triangular almost finite algebras. This set forms a topological space under the hull-kernel closure, and there is a one-to-one correspondence between closed sets in this space and ideals in the AF algebra. Some connections with nest representations and nestprimitive ideals are also described.

Quasi-triangular structures on Hopf algebras with positive bases

A basis B of a finite dimensional Hopf algebra H is said to be positive if all the structure constants of H relative to B are non-negative. A quasi triangular structure R ∈ H ⊗ H is said to be positive with respect to B if it has non-negative coefficients in the basis B ⊗ B of H ⊗ H. In our earlier work, we have classified all finite dimensional Hopf algebras with positive bases. In this paper,...

Biflatness and Biprojectivitiy of Triangular Banach Algebras

Ultra and Involution Ideals in $BCK$-algebras

In this paper, we define the notions of ultra and involution ideals in $BCK$-algebras. Then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. Specially, we show that in a bounded implicative $BCK$-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower $BCK$-semilattice, the not...