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DeMeyer, Frank R.

Generic polynomials. (English) Zbl 0521.12014

J. Algebra 84, 441-448 (1983).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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Cited in 1 Review
Cited in 15 Documents

MSC:

12F10 Separable extensions, Galois theory
12E10 Special polynomials in general fields
12E99 General field theory
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
12J10 Valued fields
11R18 Cyclotomic extensions

Keywords:

Noether problem; generic Galois extension; Grunwald-Wang theory; Hilbert fields; Hilbert irreducibility theorem; retract rational fields; cyclic Galois extensions; generic polynomial; separable field extension

Citations:

Zbl 0484.12004
Cite Review PDF
Full Text: DOI

References:

[1] Bennett, A., Generic Galois Extensions Which are Splitting Rings, (Honors Thesis (1981), Colorado State University: Colorado State University Fort Collins)
[2] Chase, S. U.; Harrison, D. K.; Rosenberg, A., Galois theory and Galois Cohomology of commutative rings, Mem. Amer. Math. Soc., 52, 15-33 (1968) · Zbl 0143.05902
[3] DeMeyer, F. R.; Ingraham, E., Separable algebras over commutative rings, (Lecture Notes in Mathematics, No. 181 (1971), Springer-Verlag: Springer-Verlag Berlin/Now York) · Zbl 0215.36602
[4] Hall, M., The Theory of Groups (1959), Macmillan: Macmillan New York · Zbl 0084.02202
[5] Janusz, G. J., Separable algebras over commutative rings, Trans Amer. Math. Soc., 122, 461-479 (1966) · Zbl 0141.03402
[6] Kuyk, W., On a theorem of E. Noether, (Nederl. Akad. Wetensch. Proc. Ser. A, 67 (1964)), 32-39 · Zbl 0166.04703
[7] Lenstra, H. W., Rational functions invariant under a finite abelian, Invent. Math., 25, 299-325 (1974) · Zbl 0292.20010
[8] Noether, E., Gleichungen mit vorgeschriebener gruppe, Math. Ann., 78 (1916) · JFM 46.0135.01
[9] Rutherford, D., Modular Invariants, Cambridge Tracts in Mathematics (1932) · JFM 58.0116.07
[10] Saltman, D., Generic Galois extensions, (Proc. Nat. Acad. Sci. U.S.A., 77 (1980)), 1250-1251 · Zbl 0445.12010
[11] Saltman, D., Generic Galois extensions and probems in field theory, Advan. in Math., 43, 250-283 (1982) · Zbl 0484.12004
[12] Saltman, D., Generic structures and field theory, (Seligman, G.; etal., Algebraists Homage (1982), Amer. Math. Soc.,: Amer. Math. Soc., Providence, R. I.) · Zbl 0503.16019
[13] Saltman, D., Retract rational fields and cyclic Galois extensions (1982), Univ. of Texas: Univ. of Texas Austin, preprint
[14] Swan, R., Invariant rational functions and a problem of Steenrod, Invant. Math., 7, 148-158 (1969) · Zbl 0186.07601
[15] Swan, R., Galois theory, (Brewer, J.; Smith, M., Emmy Noether: A Tribute to her Life and Work (1981), Dekker: Dekker New York) · Zbl 0543.01009
[16] Swan, R., Noether’s problem in Galois theory (1981), Univ. of Chicago, preprint
[17] Zariski, O.; Samuel, P., (Commutative algebra, Vol. 1 (1958), Van Nostrand: Van Nostrand Princeton, N.J.) · Zbl 0112.02902
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