Algorithmic determination of the jacobson radical of monomial algebras

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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.

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Gateva-Ivanova, T. (1989). Algorithmic determination of the jacobson radical of monomial algebras. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 378 LNCS, pp. 355–364). Springer Verlag. https://doi.org/10.1007/3-540-51517-8_139

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