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.
Partially supported by Contract No. 62/1987, Committee of Science, Bulgaria.
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References
T. Gateva-Ivanova, V. Latyshev, On recognizable properties of associative algebras, J. Symb. Comp., 1988, to appear.
V. Ufnarovskij, A growth criterion for graphs and algebras defined by words, Mat. Zametki 31 (1982), 465–472 (in Russian); English transl.: Math. Notes 37 (1982), 238–241.
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© 1989 Springer-Verlag Berlin Heidelberg
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Gateva-Ivanova, T. (1989). Algorithmic determination of the jacobson radical of monomial algebras. In: Davenport, J.H. (eds) Eurocal '87. EUROCAL 1987. Lecture Notes in Computer Science, vol 378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51517-8_139
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DOI: https://doi.org/10.1007/3-540-51517-8_139
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