A Note on Finite Ring Extensions

Abstract

finite number of elements $\omega_{1},$ $\omega_{2},$ $\cdots\omega_{n}$ of $S$ can be found such that $S=R\omega_{1}+R\omega_{2}+\cdots+Rru_{n}$ .This modul finite extension has to be distinguished from what we shall call a ring finite extensionin which every element of $S$ can be written as polynomial in the generatorswith coefficients in $R$ .If we call $S^{\prime}$ the ring of all polynomials in the indeterminates $x_{1},$ $x_{2},$ $\cdots x_{n}$ with coefficients in $R$ then $S$ is a homomorphic image of $S^{\prime}$ and the following well known lemma is immediate:

Locations

• Journal of the Mathematical Society of Japan - View - PDF