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A decomposition of a module into a direct sum of submodules. The index set for the collection of submodules is then called the grading set. Graded modules arise naturally in ...

Let S be a set of n+1 symbols, then a Howell design H(s,2n) on symbol set S is an s×s array H such that 1. Every cell of H is either empty or contains an unordered pair of ...

Let E be a set of expressions representing real, single-valued partially defined functions of one real variable. Let E^* be the set of functions represented by expressions in ...

A link invariant is a function from the set of all links to any other set such that the function does not change as the link is changed (up to isotopy). In other words, a ...

A well-formed formula B is said to be true for the interpretation M (written |=_MB) iff every sequence in Sigma (the set of all denumerable sequences of elements of the ...

A module M is Noetherian if it obeys the ascending chain condition with respect to inclusion, i.e., if every set of increasing sequences of submodules eventually becomes ...

A point x in a manifold M is said to be nonwandering if, for every open neighborhood U of x, it is true that phi^nU intersection U!=emptyset for a map phi for some n>0. In ...

An orthogonal basis of vectors is a set of vectors {x_j} that satisfy x_jx_k=C_(jk)delta_(jk) and x^mux_nu=C_nu^mudelta_nu^mu, where C_(jk), C_nu^mu are constants (not ...

If all elements a_(ij) of an irreducible matrix A are nonnegative, then R=minM_lambda is an eigenvalue of A and all the eigenvalues of A lie on the disk |z|<=R, where, if ...

A distance g on a set that fulfils the same properties as a metric except relaxes the definition to allow the distance between two different points to be zero. An example of ...