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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.
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참고문헌 (30)
참고문헌 신청
D. D. Anderson / 1990 / Factorization in integral domains / J. Pure Appl. Algebra 69(1):1~19
H. Bass / 1960 / Finitistic dimension and a homological generalization of semi-primary rings / Trans. Amer. Math. Soc 95:466~488
P. M. Cohn / 1985 / Free Rings and Their Relations / Academic Press, Inc
T. Dumitrescu / 2000 / Some factorization properties of composite domains A + XB[X] and A + XB[[X]] / Comm. Algebra 28(3):1125~1139
G. A. Elliott / 1990 / Fields of generalized power series / Arch. Math. (Basel) 54(4):365~371
H. Bass / 1960 / Finitistic dimension and a homological generalization of semi-primary rings / Trans. Amer. Math. Soc 95:466~488
P. M. Cohn / 1985 / Free Rings and Their Relations / Academic Press, Inc
T. Dumitrescu / 2000 / Some factorization properties of composite domains A + XB[X] and A + XB[[X]] / Comm. Algebra 28(3):1125~1139
G. A. Elliott / 1990 / Fields of generalized power series / Arch. Math. (Basel) 54(4):365~371
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