(mathematical analysis) The smallest σ-algebra which contains the topology of a given topological space.

(algebra) A field of sets whose elements are equivalent to Boolean formulas (or, perhaps more precisely, equivalence classes of Boolean formulas). Starting with a set of n variables which are independent of each other and are called generators, the power set of this set has 2ⁿmembers which may be called atoms and are valuations of the n variables: a valuation can be considered to be a set of variables which are "true" under that valuation, or a conjunction of generators (such that variables not included in that set are included in negated form in the equivalent conjunction). Then the power set of the set of atoms yields a set of 2^(2ⁿ) members which are the elements of the said field of sets. These elements correspond to Boolean formulas: a formula can be considered to be a set of valuations which make the formula true, or a linear combination (i.e., a disjunction) of atoms.

(algebra, logic) ring sum normal form

(algebra) A relatively new discipline in mathematics that combines techniques and concepts from combinatorics and commutative algebra, and in which the geometry of convex polytopes also plays a significant role.

(algebra, ring theory) A finite-dimensional associative algebra over some field K that is a simple algebra and whose centre is exactly K.

(algebraic geometry, category theory) An algebraic group that is isomorphic to a subgroup of some general linear group.

plural of linear algebraic group

(mathematics, algebraic number theory) A field which includes the rational numbers and has finite dimension as a vector space over the rational numbers.

(algebra, order theory) A bounded distributive lattice equipped with an involution (typically denoted ¬ or ~) which satisfies De Morgan's laws.

(algebra) An algebra over a field whose bilinear product is not necessarily associative. / (algebra) An algebra over a ring whose bilinear product is not necessarily associative.