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- W1931738480 abstract "Let $Asubset B$ be an integral ring extension of integral domains with fields of fractions $K$ and $L$, respectively. The integral degree of $Asubset B$, denoted by ${rm d}_A(B)$, 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 ${rm d}_K(L)$ and $mu_A(B)$, 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: if $Asubset B$ is simple; if $Asubset B$ is projective and finite and $Ksubset L$ is a simple algebraic field extension; or if $A$ is integrally closed. Furthermore, ${rm d}$ is semicontinuous if $A$ is noetherian of dimension $1$ and with finite integral closure. In general, however, ${rm d}$ is neither sub-multiplicative nor upper-semicontinuous." @default.
- W1931738480 created "2016-06-24" @default.
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- W1931738480 date "2015-07-08" @default.
- W1931738480 modified "2023-10-18" @default.
- W1931738480 title "On the integral degree of integral ring extensions" @default.
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