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An algebra which does not satisfy a(bc)=(ab)c is called a nonassociative algebra.

Let A denote an R-algebra, so that A is a vector space over R and A×A->A (1) (x,y)|->x·y. (2) Now define Z={x in A:x·y=0 for some y in A!=0}, (3) where 0 in Z. An Associative ...

A generalization of a Heyting algebra which replaces Boolean algebra in "intuitionistic" logic.

A finite-dimensional Lie algebra all of whose elements are ad-nilpotent is itself a nilpotent Lie algebra.

If A is a unital Banach algebra where every nonzero element is invertible, then A is the algebra of complex numbers.

An operator A^~ such that A^~^2=A^~ or an element of an algebra x such that x^2=x.

A set considered together with the sigma-algebra on the set.

A set equipped with a sigma-algebra of subsets.

A Boolean sigma-algebra which possesses a measure.

A unar is an algebra A=(A,f), where f is a single unary operation.