2002/10/14 by B. Plotkin, Plotkin, B.
Mathematics · #08A99 #18A99 #Category Theory (math.CT) #FOS: Mathematics #General Mathematics (math.GM) #math.CT #math.GM #msc:08A99 #msc:18A99
paper · pdf · doi:10.48550/arxiv.math/0210194
52 pages, cd.tex
arxiv created 2002/10/14 · arxiv updated 2009/11/30
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.