A. Tarski [4] has given a decision method for elementary algebra. In essence this comes to giving an algorithm for deciding whether a given finite set of polynomial inequalities has a solution. Below… Expand

Let k [ [X, Y]] be the ring of formal power series in two letters over an algebraically closed base field k of characteristic zero, let A, B C k [ [X, Y]] be elements without non-unit common divisor,… Expand

Let d? be an integral domain containing the rational numbers, Σ its quotient field, D a derivation of Σ, and &1 the ring of elements in Σ quasi-integral over &. It is shown that if £? then Dέ?f c &'.

covered in that investigation show, however, that we have in them a class of varieties demanding study for its own sake. Another very good, but in one sense probably more transient, reason for the… Expand