## with the same algebraic geometry (2002)

Venue: | Proceedings of the International Conference on Mathematical Logic, Algebra and Set Theory, dedicated to 100 anniversary of P.S.Novikov, Proceedings MIAN |

Citations: | 18 - 3 self |

### BibTeX

@INPROCEEDINGS{Plotkin02withthe,

author = {B. Plotkin},

title = {with the same algebraic geometry},

booktitle = {Proceedings of the International Conference on Mathematical Logic, Algebra and Set Theory, dedicated to 100 anniversary of P.S.Novikov, Proceedings MIAN},

year = {2002}

}

### OpenURL

### Abstract

Abstract. Some basic notions of classical algebraic geometry can be defined in arbitrary varieties of algebras Θ. For every algebra H in Θ one can consider algebraic geometry in Θ over H. Correspondingly, algebras in Θ are considered with the emphasis on equations and geometry. We give examples of geometric properties of algebras in Θ and of geometric relations between them. The main problem considered in the paper is when different H1 and H2 have the same geometry.