Algebras with the same (algebraic) geometry

Details Algebras with the same (algebraic) geometry Algebras with the same (algebraic) geometry

2002-10-14

arxiv.org/abs/math/0210194v1

Mathematics

General Mathematics

52 pages, cd.tex

Scientific paper

Some basic notions of classical algebraic geometry can be defined in 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.

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