A general invariant metrization theorem for compact spaces
Let be a field, and the set of monomials of . It is well known that the set of monomial ideals of is in a bijective correspondence with the set of all subsemiflows of the -semiflow . We generalize this to the case of term ideals of , where is a commutative Noetherian ring. A term ideal of is an ideal of generated by a family of terms , where and are integers .
We obtain an elementary geometrical proof of the classical Perron-Frobenius theorem for non-negative matrices A by using the Brouwer fixed-point theorem and by studying the dynamics of the action of A on convenient subsets of Rn.