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The term endomorphism derives from the Greek adverb endon ("inside") and morphosis ("to form" or "to shape"). In algebra, an endomorphism of a group, module, ring, vector ...

Let A be a C^*-algebra and A_+ be its positive part. Suppose that E is a complex linear space which is a left A-module and lambda(ax)=(lambdaa)x=a(lambdax), where lambda in ...

Throughout abstract algebra, the term "magma" is most often used as a synonym of the more antiquated term "groupoid," referring to a set equipped with a binary operator. The ...

A spectral sequence is a tool of homological algebra that has many applications in algebra, algebraic geometry, and algebraic topology. Roughly speaking, a spectral sequence ...

The use of techniques from algebra, topology, and geometry in the solution of combinatorial problems, or the use of combinatorial methods to attack problems in these areas ...

Let K be a field, and A a K-algebra. Elements y_1, ..., y_n are algebraically independent over K if the natural surjection K[Y_1,...,Y_n]->K[y_1,...,y_n] is an isomorphism. ...

If F is the Borel sigma-algebra on some topological space, then a measure m:F->R is said to be a Borel measure (or Borel probability measure). For a Borel measure, all ...

Elementary methods consist of arithmetic, geometry, and high school algebra. These are the only tools that may be used in the branch of number theory known as elementary ...

Given a subalgebra A of the algebra B(H) of bounded linear transformations from a Hilbert space H onto itself, the vector v in H is a separating vector for A if the only ...

The structure constant is defined as iepsilon_(ijk), where epsilon_(ijk) is the permutation symbol. The structure constant forms the starting point for the development of Lie ...