Communications of the
Korean Mathematical Society CKMS

Let $R$ be a ring, $(S,\leq)$ a strictly ordered monoid, and $\omega: S\rightarrow {\rm End}(R)$ a monoid homomorphism. In \cite{zim}, 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 \cite{zim}, 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.

Keywords: skew generalized power series ring, strictly ordered monoid, Archimedean ring

MSC numbers: 16P70, 16P60, 13F10, 13J05