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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