Algorithmic determination of the jacobson radical of monomial algebras

Abstract

The paper considers computer algebra in a non-commutative setting. Under investigation are finitely presented associative monomial algebras and some of their recognizable properties. In [1] it was shown that for a monomial algebra A the properties of being semi-simple (in the sense of Jacobson), prime, or semiprime are recognizable. In the paper a new interpretation of these properties is given in terms of the Ufnarovsky graph of A. This provides better algorithms for their verification. It is proved that the Jacobson radical of A is finitely generated as an ideal. It is also proved that the algebra A is semi-prime if and only if it is semi-simple in the sense of Jacobson.