High Quality Content by WIKIPEDIA articles! In universal algebraic geometry, algebraic geometry is generalized from the geometry of rings to geometry of arbitrary varieties of algebras, so that every variety of algebras has its own algebraic geometry. Note that the two terms algebraic variety and variety of algebras should not be confused. Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis, topology and number theory. Initially a study of polynomial equations in many variables, the subject of algebraic geometry starts where equation solving leaves off, and it becomes at least as important to understand the totality of solutions of a system of equations, as to find some solution; this leads into some of the deepest waters in the whole of mathematics, both conceptually and in terms of technique.

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