Algebras with the same (algebraic) geometry. (English) Zbl 1062.08012

Plotkin, B.

Proc. Steklov Inst. Math. 242, 165-196 (2003) and Tr. Mat. Inst. Im. V. A. Steklova 242, 176-207 (2003).

Summary: Some basic notions of classical algebraic geometry can be defined on arbitrary varieties of algebras \(\Theta\). For every algebra \(H\) in \(\Theta\), one can consider algebraic geometry in \(\Theta\) over \(H\). Correspondingly, algebras in \(\Theta\) are considered with the emphasis on equations and geometry. We give examples of geometric properties of algebras in \(\Theta\) and of geometric relations between them. The main problem considered in the paper is when different \(H_1\) and \(H_2\) have the same geometry.
For the entire collection see [Zbl 1059.03004].

MSC:

08B99	Varieties
14A20	Generalizations (algebraic spaces, stacks)

Keywords:

universal algebraic geometry; varieties of algebras; geometric properties of algebras