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For {M_i}_(i in I) a family of R-modules indexed by a directed set I, let sigma_(ij):M_i->M_j i<=j be an R-module homomorphism. Call (M_i,sigma_(ij)) a direct system over I ...

If the lines joining corresponding points of two directly similar figures are divided proportionally, then the locus of the points of the division will be a figure directly ...

An extreme point of a subset K of a vector space X is an extreme set S of K which consists of a single point x in K. The collection of all extreme points of K is sometimes ...

In a chain complex of modules ...->C_(i+1)->^(d_(i+1))C_i->^(d_i)C_(i-1)->..., the module B_i of i-boundaries is the image of d_(i+1). It is a submodule of C_i and is ...

The analytic summation of a hypergeometric series. Powerful general techniques of hypergeometric summation include Gosper's algorithm, Sister Celine's method, Wilf-Zeilberger ...

A quadratic form Q(x) is indefinite if it is less than 0 for some values and greater than 0 for others. The quadratic form, written in the form (x,Ax), is indefinite if ...

A particular type of automorphism group which exists only for groups. For a group G, the inner automorphism group is defined by Inn(G)={sigma_a:a in G} subset Aut(G) where ...

A triangle DeltaA^'B^'C^' is said to be inscribed in a triangle DeltaABC if A^' lies on BC, B^' lies on CA, and C^' lies on AB (Kimberling 1998, p. 184). Examples include the ...

A polynomial that represents integers for all integer values of the variables. An integer polynomial is a special case of such a polynomial. In general, every integer ...

Given a commutative unit ring R and an extension ring S, an element s of S is called integral over R if it is one of the roots of a monic polynomial with coefficients in R.