algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety fields of large transcendence degree; algebraic independence; zero lemmas; zero estimate for group varieties; primary ideal; polynomial rings; algebraic subgroups of products of elliptic curves; effective version of Hilbert's Nullstellensatz; Kolchin theorem; Weierstrass elliptic function 