A fancy way to say commutative (honoring N. H. Abel). In an abelian group , xy = yx for any arbitrary choice of x and y.
The ideal generated by a set in a vector space.
Over any finite field F one can construct a two-dimensional affine geometry. If the field is of size n, the affine plane consists of a set P of points which are ordered pairs of elements of the field (thus there are n2 points), and a set L of lines which are themselves sets of points. The points on a given line consist of all pairs (x,y) which are solutions of a linear equation ( y=mx+b , or x=k, with m,b and k in F). The lines can be further divided up into "parallel classes" based on the value of m in their defining equation, (the lines of the form x=k are said to be in the "infinite slope" parallel class).
By adding an additional "point at infinity" for each of the parallel classes and an additional "line at infinity" which connects the points at infinity, one can construct a projective plane from an affine plane.
A digraph D is an arborescence if there is a distinguished node x (called the root) and for every node y different from x there is exactly one elementary path from x to y.
The partition of space into cells formed by overlaying a collection of surfaces (often hyperplanes).