Extensions of associative algebras

Identities of Associative Algebras

The structure theory for Pi-algebras is well developed. Some results of this theory are classic now. One of them is Kaplansky's theorem which asserts that a primitive Pi-algebra is finite dimensional over its centre. Another example is the theorem of Nagata-Higman which asserts that any algebra over a field of zero characteristic satisfying identity x" = 0 is nilpotent. In 1957 A.I. Shirshov pr...

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

Non Associative Linear Algebras

Non-associative algebras associated to Poisson algebras

Poisson algebras are usually defined as structures with two operations, a commutative associative one and an anti-commutative one that satisfies the Jacobi identity. These operations are tied up by a distributive law, the Leibniz rule. We present Poisson algebras as algebras with one operation, which enables us to study them as part of non-associative algebras. We study the algebraic and cohomo...