Let O∗ be the C-algebra defined as the direct sum of all Cuntz algebras. Then O∗ has a non-cocommutative comultiplication ∆φ and a counit ε. Let BI(O∗) denote the set of all closed biideals of the C-bialgebra (O∗,∆φ, ε) and let P(P) denote the power set of the set of all prime numbers. We show a one-to-one correspondence between BI(O∗) and P(P). Furthermore, we show that for any I in BI(O∗), th...

We consider projectivity and injectivity of Hilbert C*-modules in the categories of Hilbert C*-(bi-)modules over a fixed C*-algebra of coefficients (and another fixed C*-algebra represented as bounded module operators) and bounded (bi-)module morphisms, either necessarily adjointable or arbitrary ones. As a consequence of these investigations, we obtain a set of equivalent conditions characteri...

The theory of Amalgamated Knowledge' Bases [7] represents a formal logical foundation for heterogeneous databases. In an Amalgamated Knowledge Base, data sources are modeled by generalized annotated logic. Moreover, an Amalgamated Knowledge Base is equipped with a supervisor acting as a mediator for amalgamating knowledge from the local databases. Even if the framework is quite appealing, it do...

Residually thin and nilpotent table algebras, which are abstractions of fusion rings adjacency algebras association schemes, defined investigated. A formula for the degrees basis elements in residually is established, yields an integrality result Gelaki Nikshych as immediate corollary; it shown that this holds only such algebras. These theorems specialize to new results schemes. Bi-anchored thi...

1.a. Since its introduction by Kazhdan in [Ka], property (T ) became a fundamental concept in mathematics with a wide range of applications to such areas as: • The structure of infinite groups—finite generation and finite Abelianization of higher-rank lattices [Ka], obstruction to free or amalgamated splittings [Wa], [A], [M4], structure of normal subgroups [M2] etc.; • Combinatorics—the first ...