A generalization of a theorem of Ore

作者：Khanduja Sudesh K^*; Kumar Sanjeev

来源：Journal of Pure and Applied Algebra, 2014, 218(7): 1206-1218.

DOI：10.1016/j.jpaa.2013.11.014

Let (K, v) be a discrete rank one valued field with valuation ring R-v. Let L/K be a finite extension such that the integral closure S of R-v in L is a finitely generated R-v-module. Under a certain condition of v-regularity, we obtain some results regarding the explicit computation of R-v-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.

• 出版日期2014-7