Coherent extensions and relational algebras

Coherent Algebras

Coherent algebras are defined to be the subalgebras of the matrix algebras M,(C) closed under Hadamard ( = coefficientwise) multiplication and containing the all 1 matrix, and are shown to be precisely the adjacency algebras of coherent confignrations. Each such algebra has a type, which is a symmetric matrix with positive integer entries. The theory is illustrated by applications to quasisymme...

Relational Algebras

Extensions of Topological Algebras

We prove that, in the class of commutative topological algebras with separately continuous multiplication, an element is permanently singular if and only if it is a topological divisor of zero. This extends the result given by R. Arens [1] for the Banach algebra case. We also give sufficient conditions for non-removability of ideals in commutative topological algebras with jointly continuous mu...

Extensions of Normed Algebras

(Minor corrections and additions have been made. The page layout has also been changed.) 0 Contents Contents 1 Abstract 2 Chapter 1: Constructions and Elementary Properties and Applications of Algebraic Extensions of Normed Algebras 3

Cylindric algebras and relational databases

An interpretation of the relational data model and various dependencies is given within the framework of cylindric algebras. It turns out that there is a natural translation of relational databases into cylindric set lattices, and that Codd’s relational operators have a simple interpretation in these structures. Consequently, various database constraints can be expressed in the equational langu...