(algebraic geometry) A subset of an algebraic variety that is itself an algebraic variety.

plural of algebraic subvariety

(algebraic geometry) The set of solutions of a given system of polynomial equations over the real or complex numbers; any of certain generalisations of such a set that preserves the geometric intuition implicit in the original definition.

plural of simple algebra

(algebra) An algebra that contains no nontrivial proper (two-sided) ideals and whose multiplication operation is not zero (i.e., there exist a and b such that ab ≠ 0).

plural of algebraic group

(algebraic geometry) A group that is an algebraic variety.

(algebra, ring theory) An algebra over a reduced ring.

plural of reduced algebra

plural of algebraic extension