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(t, v)-Dedekind Domains and the Ring \({{R[X]_{N_v}}}\)

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Abstract

Let R be an integral domain and X an indeterminate over R. In this paper, we indicate that the quotient ring of a (t, v)-Dedekind domain is not necessarily a (t, v)-Dedekind domain. Also, we show that a locally (t, v)-Dedekind domain is not necessarily a (t, v)-Dedekind domain. The characterization of the localization of a (t, v)-Dedekind domain further leads us to study the quotient ring \({R[X]_{N_v}}\) over a (t, v)-Dedekind domain R. As the application of the ring \({R[X]_{N_v}}\), we end this paper by characterizing the group ring R[X; G] and the semigroup ring R[Γ] over a (t, v)-Dedekind domain R.

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Authors and Affiliations

  1. Institute of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610068, People’s Republic of China

    Qing Li

  2. College of Computer Science and Technology, Southwest University for Nationalities, Chengdu, 610041, People’s Republic of China

    Qing Li

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  1. Qing Li
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Correspondence to Qing Li.

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Li, Q. (t, v)-Dedekind Domains and the Ring \({{R[X]_{N_v}}}\) . Results. Math. 59, 91–106 (2011). https://doi.org/10.1007/s00025-010-0061-1

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  • DOI: https://doi.org/10.1007/s00025-010-0061-1

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