Transcendence bases for field extensions

James K. DEVENEY; John N. MORDESON

doi:10.2969/jmsj/03440703

James K. DEVENEY, John N. MORDESON

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JOURNAL FREE ACCESS

1982 Volume 34 Issue 4 Pages 703-707

DOI https://doi.org/10.2969/jmsj/03440703

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Published: 1982 Received: July 29, 1980 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) P. Blass, Zariski surfaces, Ph. D, dissertation, The University of Michigan, 1977.
2) J. Deveney, Generalized primitive elements for transcendental field extensions, Pacific J. Math., 68 (1977), 41-45.
3) J. Deveney and J. Mordeson, Subfields and invariants of inseparable field extensions, Canad. J. Math., 29 (1977), 1304-1311.
4) J. Deveney and J. Mordeson, The order of inseparability of fields, Canad. J. Math., 31 (1979), 655-662.
5) J. Deveney and J. Mordeson, Distinguished subfields, Trans. Amer. Math. Soc., (to appear).
6) J. Deveney and J. Mordeson, Calculating invariants of inseparable field extensions, (to appear).
7) J. Deveney and J. Mordeson, Distinguished subfields of intermediate fields, preprint.
8) J. Dieudonné, Sur les extensions transcendantes séparables, Summa Brasil. Math., 2 (1947), 1-20.
9) N. Heerema, p-th power of distinguished subfields, Proc. Amer. Math. Soc., 55 (1976), 287-292.
10) T. Kambayashi and M. Miyanishi, On forms of the affine line over a field, Lectures in Math., Dept. of Math. Kyoto Univ., 10, Kinokuniya, Tokyo, Japan, 1977.
11) H. Kraft, Inseparable Körpererweiterungen, Comment. Math. Helv., 45 (1970), 110-118.
12) T. Moh and W. Heinzer, A generalized Luroth theorem for curves, J. Math. Soc. Japan, 31 (1979), 85-86.
13) T. Moh and W. Heinzer, On the Luroth semigroup and Weierstrass canonical divisors, preprint.
14) J. Mordeson, Splitting of field extensions, Arch. Math. (Basel), 26 (1975), 606-610.
15) J. Mordeson and B. Vinograde, Separating p-bases and transcendental extension fields, Proc. Amer. Math. Soc., 31 (1972), 417-422.
16) J. Mordeson and B. Vinograde, Inseparable embeddings of separable transcendental extensions, Arch. Math. (Basel), 27 (1976), 42-47.
17) P. Roquette, Isomorphisms of generic splitting fields of simple algebras, J. Reine Angew. Math., 214/215 (1963), 207-226.
18) A. Rudakov and I. Safarevic, Inseparable morphisms of algebraic surfaces, Math. USSR-Izv., 10 (1976), 1205-1237.
19) A. Weil, Foundations of algebraic geometry, Amer. Math. Soc. Colloq. Publ., 29, Amer. Math. Soc., Providence, R.I., 1946.

Right : [1] P. Blass, Zariski surfaces, Ph. D, dissertation, The University of Michigan, 1977.
[2] J. Deveney, Generalized primitive elements for transcendental field extensions, Pacific J. Math., 68 (1977), 41-45.
[3] J. Deveney and J. Mordeson, Subfields and invariants of inseparable field extensions, Canad. J. Math., 29 (1977), 1304-1311.
[4] J. Deveney and J. Mordeson, The order of inseparability of fields, Canad. J. Math., 31 (1979), 655-662.
[5] J. Deveney and J. Mordeson, Distinguished subfields, Trans. Amer. Math. Soc., (to appear).
[6] J. Deveney and J. Mordeson, Calculating invariants of inseparable field extensions, (to appear).
[7] J. Deveney and J. Mordeson, Distinguished subfields of intermediate fields, preprint.
[8] J. Dieudonné, Sur les extensions transcendantes séparables, Summa Brasil. Math., 2 (1947), 1-20.
[9] N. Heerema, p-th power of distinguished subfields, Proc. Amer. Math. Soc., 55 (1976), 287-292.
[10] T. Kambayashi and M. Miyanishi, On forms of the affine line over a field, Lectures in Math., Dept. of Math. Kyoto Univ., 10, Kinokuniya, Tokyo, Japan, 1977.
[11] H. Kraft, Inseparable Körpererweiterungen, Comment. Math. Helv., 45 (1970), 110-118.
[12] T. Moh and W. Heinzer, A generalized Luroth theorem for curves, J. Math. Soc. Japan, 31 (1979), 85-86.
[13] T. Moh and W. Heinzer, On the Luroth semigroup and Weierstrass canonical divisors, preprint.
[14] J. Mordeson, Splitting of field extensions, Arch. Math. (Basel), 26 (1975), 606-610.
[15] J. Mordeson and B. Vinograde, Separating p-bases and transcendental extension fields, Proc. Amer. Math. Soc., 31 (1972), 417-422.
[16] J. Mordeson and B. Vinograde, Inseparable embeddings of separable transcendental extensions, Arch. Math. (Basel), 27 (1976), 42-47.
[17] P. Roquette, Isomorphisms of generic splitting fields of simple algebras, J. Reine Angew. Math., 214/215 (1963), 207-226.
[18] A. Rudakov and I. Safarevic, Inseparable morphisms of algebraic surfaces, Math. USSR-Izv., 10 (1976), 1205-1237.
[19] A. Weil, Foundations of algebraic geometry, Amer. Math. Soc. Colloq. Publ., 29, Amer. Math. Soc., Providence, R. I., 1946.

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