The theorem of the primitive element for a semi-local ring.
The main result is an extension to semi-local rings of the theorem of the primitive element for separable extensions (of finite type) of a local ring with infinite residue field. Thus it is shown that if \(A,{\mathfrak r}\) is a semilocal ring with \(A/{\mathfrak r}\) the product of fields \(k_ 1\times\dots\times k_ r\), then every separable extension of \(A\) of rank \(m\) is simple if and only if \(\text{Card}\,k_ i\geq m\) for \(i=1,\dots,r\). The note ends with some consequences for small values of \(m\).
scientific article; zbMATH DE number 3977119
scientific article