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## On the integral degree of integral ring extensions

Author
Giral, J.M.; O'Carroll, L.; Planas-Vilanova, F. A.; Plans, B.
Type of activity
Journal article
Journal
Proceedings of the Edinburgh Mathematical Society
Date of publication
2019-02-01
Volume
62
Number
1
First page
25
Last page
46
DOI
https://doi.org/10.1017/S0013091518000275
Repository
http://hdl.handle.net/2117/127519
URL
https://www.cambridge.org/core/journals/proceedings-of-the-edinburgh-mathematical-society/article/on-the-integral-degree-of-integral-ring-extensions/4669AAC5255996C714C9CB482BE6FDE1
Abstract
Let A ¿ B be an integral ring extension of integral domains with fields of fractions K and L, respectively. The integral degree of A ¿ B, denoted by dA(B), is defined as the supremum of the degrees of minimal integral equations of elements of B over A. It is an invariant that lies in between dK(L) and µA(B), the minimal number of generators of the A-module B. Our purpose is to study this invariant. We prove that it is sub-multiplicative and upper-semicontinuous in the following three cases: i...
Citation
Giral, J.M. [et al.]. On the integral degree of integral ring extensions. "Proceedings of the Edinburgh Mathematical Society", 1 Febrer 2019, vol. 62, núm. 1, p. 25-46.
Group of research
GEOMVAP - Geometry of Manifolds and Applications