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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Separable criteria for $ G$-diagrams over commutative rings


Author: Charles Winfred Roark
Journal: Proc. Amer. Math. Soc. 63 (1977), 1-5
MSC: Primary 16A74; Secondary 16A16, 13B05
MathSciNet review: 0437609
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Abstract | References | Similar Articles | Additional Information

Abstract: Let S be a commutative, separable algebra over the commutative ring R and finitely generated and projective as an R-module. Suppose G is a group of ring automorphisms of S stabilizing R setwise. It is shown that for the ring of invariants $ {S^G}$ to be a strongly separable extension of $ {R^G}$ it is necessary that $ R \cdot {S^G}$ be R-separable; and it is shown that this condition is sufficient when R and S are finitely generated algebras over an algebraically closed field and G is a linearly reductive algebraic group acting rationally on S.


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

  • [B] N. Bourbaki, Commutative algebra, English transl., Hermann, Paris; Addison-Wesley, Reading, Mass., 1972. MR 50 #12997. MR 0360549 (50:12997)
  • [DI] F. B. DeMeyer and E. Ingraham, Separable algebras over commutative rings, Lecture Notes in Math., vol. 181, Springer-Verlag, Berlin and New York, 1971. MR 43 #6199. MR 0280479 (43:6199)
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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0437609-2
PII: S 0002-9939(1977)0437609-2
Keywords: Separable algebra, Galois extension, linearly reductive algebraic group, rational G-module, G-ergodic
Article copyright: © Copyright 1977 American Mathematical Society



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