Fields of constants of infinite higher derivations

Author:
James K. Deveney

Journal:
Proc. Amer. Math. Soc. **41** (1973), 394-398

MSC:
Primary 12F10; Secondary 12F15

MathSciNet review:
0335478

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Abstract: Let be a field of characteristic , and let be its maximal perfect subfield. Let be a subfield of containing such that is separable over . We prove: Every regular subfield of containing is the field of constants of a set of higher derivations on if and only if (1) the transcendence degree of over is finite, and (2) has a separating transcendency basis over . This result leads to a generalization of the Galois theory developed in [**4**].

**[1]**Nickolas Heerema,*Convergent higher derivations on local rings*, Trans. Amer. Math. Soc.**132**(1968), 31–44. MR**0223358**, 10.1090/S0002-9947-1968-0223358-1**[2]**Nickolas Heerema,*Derivations and embeddings of a field in its power series ring. II*, Michigan Math. J.**8**(1961), 129–134. MR**0136601****[3]**Morris Weisfeld,*Purely inseparable extensions and higher derivations*, Trans. Amer. Math. Soc.**116**(1965), 435–449. MR**0191895**, 10.1090/S0002-9947-1965-0191895-1**[4]**Nickolas Heerema and James Deveney,*Galois theory for fields 𝐾/𝑘 finitely generated*, Trans. Amer. Math. Soc.**189**(1974), 263–274. MR**0330124**, 10.1090/S0002-9947-1974-0330124-8**[5]**Saunders Mac Lane,*Modular fields. I. Separating transcendence bases*, Duke Math. J.**5**(1939), no. 2, 372–393. MR**1546131**, 10.1215/S0012-7094-39-00532-6

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1973-0335478-9

Keywords:
Higher derivation,
regular extension field

Article copyright:
© Copyright 1973
American Mathematical Society