COMPOSITE HURWITZ RINGS AS ARCHIMEDEAN RINGS
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초록
Let D ⊆ E be an extension of integral domains with char- acteristic zero, I be a nonzero proper ideal of D, and let H(D,E) and H(D,I) (resp., h(D,E) and h(D,I)) be composite Hurwitz series rings (resp., composite Hurwitz polynomial rings). In this article, we show that H(D, E) is an Archimedean ring if and only if h(D, E) is an Archimedean ring, if and only if n≥1 dnE = (0) for each nonzero nonunit d in D. We also prove that H(D, I) is an Archimedean ring if and only if h(D, I) is an Archimedean ring, if and only if D is an Archimedean ring.
Abstract
Let D ⊆ E be an extension of integral domains with char- acteristic zero, I be a nonzero proper ideal of D, and let H(D,E) and H(D,I) (resp., h(D,E) and h(D,I)) be composite Hurwitz series rings (resp., composite Hurwitz polynomial rings). In this article, we show that H(D, E) is an Archimedean ring if and only if h(D, E) is an Archimedean ring, if and only if n≥1 dnE = (0) for each nonzero nonunit d in D. We also prove that H(D, I) is an Archimedean ring if and only if h(D, I) is an Archimedean ring, if and only if D is an Archimedean ring.
참고문헌 (5)
- A. Benhissi, "Basic properties of Hurwitz series rings", Ric. Mat, 61, pp.255~273 (2012)
- "Comm. Algebra", 2000, 1125~1139
- A. Hurwitz, "Sur un theoreme de M. Hadamard", C. R. Acad. Sci. Paris Ser. I Math, 128, pp.350~353 (1899)
- W.F. Keigher, "On the ring of Hurwitz series", Comm. Algebra, 25, pp.1845~1859 (1997)
- 임정욱, "Composite Hurwitz Rings Satisfying the Ascending Chain Condition on Principal Ideals", Kyungpook Mathematical Journal, 56(4), pp.1115~1123 (2016), 경북대학교 자연과학대학 수학과