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A functor between categories of groups or modules is called exact if it preserves the exactness of sequences, or equivalently, if it transforms short exact sequences into ...

The formal term used for a collection of objects. It is denoted {a_i}_(i in I) (but other kinds of brackets can be used as well), where I is a nonempty set called the index ...

The finite group T is one of the three non-Abelian groups of order 12 (out of a total of fives groups of order 12), the other two being the alternating group A_4 and the ...

A group is called a free group if no relation exists between its group generators other than the relationship between an element and its inverse required as one of the ...

If A is a graded module and there exists a degree-preserving linear map phi:A tensor A->A, then (A,phi) is called a graded algebra. Cohomology is a graded algebra. In ...

The square of a graph is defined as its second graph power. The square of any biconnected graph is Hamiltonian (Fleischner 1974, Skiena 1990, p. 231). Mukhopadhyay (1967) has ...

Let H be a Hilbert space and (e_i)_(i in I) is an orthonormal basis for H. The set S(H) of all operators T for which sum_(i in I)||Te_i||^2<infty is a self-adjoint ideal of ...

There are at least two distinct (though related) notions of the term Hilbert algebra in functional analysis. In some literature, a linear manifold A of a (not necessarily ...

An identity is a mathematical relationship equating one quantity to another (which may initially appear to be different).

An integrating factor is a function by which an ordinary differential equation can be multiplied in order to make it integrable. For example, a linear first-order ordinary ...