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

## Abstract

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.

Item Type: | Article |
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Source: | Copyright of this article belongs to Elsevier Science. |

ID Code: | 112140 |

Deposited On: | 23 Jan 2018 12:19 |

Last Modified: | 23 Jan 2018 12:19 |

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