## Abstract

The paper is related to the field which we call Universal Algebraic Geometry (UAG). All algebras under consideration belong to a variety of algebras Θ. For an arbitrary Θ we construct a system of notions which lead to a bunch of new problems. As a rule, their solutions depend on the choice of specific Θ. It can be the variety of groups Grp, the variety of associative or Lie algebras, etc. In particular, it can be the classical variety Com−P of commutative and associative algebras with a unit over a field.

For example, the paper concerns with the following general problem. For every algebra H∈Θ one can define the category of algebraic sets over H. Given H1 and H2 in Θ, the question is what are the relations between these algebras that provide an isomorphism of the corresponding categories of algebraic sets. Similar problem stands with respect to the situation when algebras are replaced by models and categories of algebraic sets are replaced by categories of definable sets. The results on the stated problem are applicable to knowledge theory and, in particular, to knowledge bases.

For example, the paper concerns with the following general problem. For every algebra H∈Θ one can define the category of algebraic sets over H. Given H1 and H2 in Θ, the question is what are the relations between these algebras that provide an isomorphism of the corresponding categories of algebraic sets. Similar problem stands with respect to the situation when algebras are replaced by models and categories of algebraic sets are replaced by categories of definable sets. The results on the stated problem are applicable to knowledge theory and, in particular, to knowledge bases.

Original language | American English |
---|---|

Pages (from-to) | 112-122 |

Journal | Труды Института математики |

Volume | 23 |

Issue number | 2, |

State | Published - 2015 |