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Given an affine variety V in the n-dimensional affine space K^n, where K is an algebraically closed field, the coordinate ring of V is the quotient ring ...

The Gosper island (Mandelbrot 1977), also known as a flowsnake (Gardner 1989, p. 41), is a fractal that is a modification of the Koch snowflake. The term "Gosper island" was ...

A family of operators mapping each space M_k of modular forms onto itself. For a fixed integer k and any positive integer n, the Hecke operator T_n is defined on the set M_k ...

The invertible matrix theorem is a theorem in linear algebra which gives a series of equivalent conditions for an n×n square matrix A to have an inverse. In particular, A is ...

The most general form of this theorem states that in a commutative unit ring R, the height of every proper ideal I generated by n elements is at most n. Equality is attained ...

A fractal curve, also called the C-curve (Gosper 1972). The base curve and motif are illustrated below. Duvall and Keesling (1999) proved that the Hausdorff dimension of the ...

The Littlewood conjecture states that for any two real numbers x,y in R, lim inf_(n->infty)n|nx-nint(nx)||ny-nint(ny)|=0 where nint(z) denotes the nearest integer function. ...

The length of all composition series of a module M. According to the Jordan-Hölder theorem for modules, if M has any composition series, then all such series are equivalent. ...

A partially ordered set (or poset) is a set taken together with a partial order on it. Formally, a partially ordered set is defined as an ordered pair P=(X,<=), where X is ...

A projective space is a space that is invariant under the group G of all general linear homogeneous transformation in the space concerned, but not under all the ...