On P-Galois extensions of rings of cyclic type (Q804678)

Let B be a ring with identity and A a subring of B with common identity 1 of B. Let P denote a cyclic relative sequence of homomorphisms in \(End(B_ A)\). The first section of this paper is concerned with the structure of B when B is a P-Galois extension over A. In particular, it is shown that if A is an algebra over a prime field of characteristic p and B is an extension ring of A, then B/A is a P-Galois extension for some P if and only if \(B=A[x]=\sum^{p-1}_{i=0}\oplus x^ iA\) is a p- extension with \(x^ p=xa+b\), where a, b are elements of A and a is an element of \(A^{p-1}\). In the second section, the author examines embedding a p-extension B/A into an S-Galois extension T/A for some relative sequence of homomorphisms S.