Algebras with the same (algebraic) geometry
By Boris I. Plotkin. 2002
116 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/02dd0c053b930399d3d1ac814af087b6386d43d8
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Geometry and Topology
- E. Daniyarova
- Alexei G. Myasnikov
- Vladimir Nikanorovich Remeslennikov
- Boris I. Plotkin
- Olga Kharlampovich
- N. Romanovskiy
- Nikolay S. Romanovskii
- Jorge Almeida
In Mathematical Physics
- Alexei G. Myasnikov
- E. Daniyarova
- Vladimir Nikanorovich Remeslennikov
- Boris I. Plotkin
- Olga Kharlampovich
- N. Romanovskiy
- Nikolay S. Romanovskii
- Jorge Almeida
Citations in the corpus
- Seven Lectures on the Universal Algebraic Geometry (2002, background): “ semiisomorphism of P-algebras. All this was done for the variety Var−P. 3Since the problem 3 is solved positively (E.Formanek [For]), the conjecture is true. 4This problem is considered in the paper [Pl11] LECTURE 5 47 Now we consider the general situation. We take varieties of the type ΘG = Θ − Ga”
- Algebraic geometry over algebraic structures III: Equationally Noetherian property and compactness (2010, background): “Plotkin [22, 23, 24] and papers on algebraic geometry over groups by G.”