ON AN EXAMPLE OF FINITEDIMENSIONAL ALGEBRAS

Abstract

An algebra \(A\) over a field \(K\) can be finitedimensional or infinitedimensional. If the multiplication in \(A\) is commutative than the algebra \(A\) itself is said to be commutative.

In this paper we formulate two theorems: the first theorem concerns the commutative finitedimensional algebras and the second one, in fact, generalizes one example of Banach algebras whose factor algebra is finitedimensional and is of the type described in the first theorem.