A generalization of a theorem of Ore

Khanduja, Sudesh K. ; Kumar, Sanjeev (2014) A generalization of a theorem of Ore Journal of Pure and Applied Algebra, 218 (7). pp. 1206-1218. ISSN 0022-4049

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/j.jpaa.2013.11.014


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

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