In Artin [l, pp. 51-75] the affine plane is developed and coordinatized from a system of four axioms. The present paper also develops affine plane geometry from a system of four axioms. The first three are the same as Artin's. The fourth is concerned with parallel projections from lines to lines. It leads to a construction of a skew field in a fashionâ€¦ (More)

An algebraic equivalent of the four-color theorem is presented. The equivalent is the assertion of non-membership of a family of polynomials in a family of polynomial ideals over a particular finite field. A more precise statement must wait until specialized machinery has been introduced. Geometry and algebra give to airy nothing a local habitation and aâ€¦ (More)