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

Let P be a class of (universal) algebras. Then an algebra A is a local P-algebra provided that every finitely generated subalgebra F of A is a member of the class P. Note ...

An algebra, also called a nilalgebra, consisting only of nilpotent Elements.

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 identity element of an additive monoid or group or of any other algebraic structure (e.g., ring, module, abstract vector space, algebra) equipped with an addition. It is ...

The Risch algorithm is a decision procedure for indefinite integration that determines whether a given integral is elementary, and if so, returns a closed-form result for the ...

In logic, the term "homomorphism" is used in a manner similar to but a bit different from its usage in abstract algebra. The usage in logic is a special case of a "morphism" ...

The l^2-norm (also written "l^2-norm") |x| is a vector norm defined for a complex vector x=[x_1; x_2; |; x_n] (1) by |x|=sqrt(sum_(k=1)^n|x_k|^2), (2) where |x_k| on the ...

Let L be a language of first-order predicate logic, let I be an indexing set, and for each i in I, let A_i be a structure of the language L. Let u be an ultrafilter in the ...