Height of separable algebras over commutative rings

Lawrence W. Naylor
1981 Rocky Mountain Journal of Mathematics  
In this paper we define an ^-algebra S to be height one separable over R (a commutative ring) if S is separable at each localization at a height one prime ideal of R. We prove some general properties of height one separability and give some examples of non-separable, height one separable extensions. It is also shown that if S is an integrally closed domain and R is the fixed subring of G-invariant elements of S, for some finite group G of automorphisms of S, and if each localization of R at a
more » ... ight 1 prime ideal in R is Noetherian, then S is a height one Galois extension (i.e., each localization at a height one prime ideal of R yields a Galois extension) if and only if S is unramified at each minimal prime ideal in S.
doi:10.1216/rmj-1981-11-4-593 fatcat:bvwswirv2nhgnfvri7kkwvjngm