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Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 18, No. 1, pp. 1-6 (2002)
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Subalgebra bases and recognizable properties

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Casapenko Louisa U.

Ulyanovsk State University, Russia

**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).

**Keywords:** Standard basis, SAGBI-basis, algorithmically recognizable properties of subalgebras in monomial algebras.

**Classification (MSC2000):** 16Z05

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