Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

An imbedding theorem for separable algebras


Author: Takasi Nagahara
Journal: Proc. Amer. Math. Soc. 41 (1973), 399-402
MSC: Primary 13B05
DOI: https://doi.org/10.1090/S0002-9939-1973-0323775-2
MathSciNet review: 0323775
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ S/R$ be a ring extension, where $ S$ is a commutative ring. If $ S/R$ is strongly separable then it can be imbedded in a weakly Galois extension of $ R$ in the sense of [7, Definition 3.1].


References [Enhancements On Off] (What's this?)

  • [1] M. Auslander and O. Goldman, The Brauer group of a commutative ring, Trans. Amer. Math. Soc. 97 (1960), 367-409. MR 22 #12130. MR 0121392 (22:12130)
  • [2] N. Bourbaki, Éléments de mathématique. Fasc. XXVII. Algèbre commutative. Chap. 1: Modules plats. Chap. 2: Localisation, Actualités Sci. Indust., no. 1290, Hermann, Paris, 1961. MR 36 #146.
  • [3] S. U. Chase, D. K. Harrison and Alex Rosenberg, Galois theory and Galois cohomology of commutative rings, Mem. Amer. Math. Soc. No. 52 (1965), 15-33. MR 33 #4118. MR 0195922 (33:4118)
  • [4] G. J. Janusz, Separable algebras over commutative rings, Trans. Amer. Math. Soc. 122 (1966), 461-479. MR 35 #1585. MR 0210699 (35:1585)
  • [5] A. R. Magid, The separable closure of some commutative rings, Trans. Amer. Math. Soc. 170 (1972), 109-124. MR 0311642 (47:204)
  • [6] T. Nagahara, A note on Galois theory of commutative rings, Proc. Amer. Math. Soc. 18 (1967), 334-340, MR 34 #7580. MR 0207765 (34:7580)
  • [7] O. E. Villamayor and D. Zelinsky, Galois theory with infinitely many idempotents, Nagoya Math. J. 35 (1969), 83-98. MR 39 #5555. MR 0244238 (39:5555)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13B05

Retrieve articles in all journals with MSC: 13B05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0323775-2
Keywords: Separable algebra, Galois, weakly Galois, imbedding
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society