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A set equipped with a sigma-algebra of subsets.

Every Lie algebra L is isomorphic to a subalgebra of some Lie algebra A^-, where the associative algebra A may be taken to be the linear operators over a vector space V.

A graded algebra over the integers Z. Cohomology of a space is a graded ring.

Let A be a unital C^*-algebra, then an element u in A is called an isometry if u^*u=1.

Let A be a C^*-algebra, then an element a in A is called normal if aa^*=a^*a.

Let A be a C^*-algebra, then an element u in A is called a partial isometry if uu^*u=u.

The root lattice of a semisimple Lie algebra is the discrete lattice generated by the Lie algebra roots in h^*, the dual vector space to the Cartan subalgebra.

The application of characteristic p methods in commutative algebra, which is a synthesis of some areas of commutative algebra and algebraic geometry.

A measure algebra which has many properties associated with the convolution measure algebra of a group, but no algebraic structure is assumed for the underlying space.

The Gelfand-Naimark theorem states that each C^*-algebra is isometrically *-isomorphic to a closed *-subalgebra of the algebra B(H) consisting of all bounded operators acting ...