ARCHIMEDEAN SKEW GENERALIZED POWER SERIES RINGS

Let R be a ring, (S, <=) a strictly ordered monoid, and omega : S -> End(R) a monoid homomorphism. In [18], Mazurek, and Ziembowski investigated when the skew generalized power series ring R[[S, omega]] is a domain satisfying the ascending chain condition on principal left (resp. right) ideals. Following [18], we obtain necessary and sufficient conditions on R, S and omega such that the skew generalized power series ring R[[S, omega]] is a right or left Archimedean domain. As particular cases of our general results we obtain new theorems on the ring of arithmetical functions and the ring of generalized power series. Our results extend and unify many existing results.