Subalgebra bases and recognizable properties

Casapenko, Louisa U. (2002) Subalgebra bases and recognizable properties. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 18 (1). pp. 1-6. ISSN 0866-0174

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Abstract

The paper considers computer algebra in a non-commutative setting. The theory of Gröbner bases of ideals in polynomial rings gives the possibility of obtaining a series of effective algorithms for symbolic calculations. Recognizable properties of associative finitely presented algebras with the finite Gröbner basis were investigated by V. N. Latyshev, T. Gateva-Ivanova in \cite{gatlat}. While subalgebras may not be as important as ideals, they are the second major type of \emph{subobject} in ring theory. The paper considers recognizable properties of subalgebras with finite standard basis, or SAGBI-basis (Subalgebra Analogue to Gröbner Basis for Ideals).

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