کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4596198 | 1336155 | 2014 | 13 صفحه PDF | دانلود رایگان |
Let (K,v)(K,v) be a discrete rank one valued field with valuation ring RvRv. Let L/KL/K be a finite extension such that the integral closure S of RvRv in L is a finitely generated RvRv-module. Under a certain condition of v -regularity, we obtain some results regarding the explicit computation of RvRv-bases of S, thereby generalizing similar results that had been obtained for algebraic number fields in El Fadil et al. (2012) [7]. The classical Theorem of Index of Ore is also extended to arbitrary discrete valued fields. We give a simple counter example to point out an error in the main result of Montes and Nart (1992) [12] related to the Theorem of Index and give an additional necessary and sufficient condition for this result to be valid.
Journal: Journal of Pure and Applied Algebra - Volume 218, Issue 7, July 2014, Pages 1206–1218