Separable criteria for $G$-diagrams over commutative rings
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- by Charles Winfred Roark PDF
- Proc. Amer. Math. Soc. 63 (1977), 1-5 Request permission
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
- Nicolas Bourbaki, Elements of mathematics. Commutative algebra, Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass., 1972. Translated from the French. MR 0360549
- Frank DeMeyer and Edward Ingraham, Separable algebras over commutative rings, Lecture Notes in Mathematics, Vol. 181, Springer-Verlag, Berlin-New York, 1971. MR 0280479, DOI 10.1007/BFb0061226
- John Fogarty, Invariant theory, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0240104
- G. J. Janusz, Separable algebras over commutative rings, Trans. Amer. Math. Soc. 122 (1966), 461–479. MR 210699, DOI 10.1090/S0002-9947-1966-0210699-5
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 63 (1977), 1-5
- MSC: Primary 16A74; Secondary 16A16, 13B05
- DOI: https://doi.org/10.1090/S0002-9939-1977-0437609-2
- MathSciNet review: 0437609