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A Note on an Equivalence Relation on aPurely Inseparable Field Extension

Published online by Cambridge University Press:  20 November 2018

P. Rygg  and
B. Lehman
P. Rygg
Affiliation:
Western Washington State College
B. Lehman
Affiliation:
Iowa State University
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We assume F is a purely inseparable field extension of the field K. The characteristic of K is p ≠ 0, and we assume F and K are not perfect. For x ∈ F, the exponent of x over K is the smallest

non-negative integer e such that and will be denoted by

e (x); ⨱ will denote . For any subset S of F, e(x; S) will denote the exponent of x over K(S); in case S = {y} we will write e(x; y) for e(x; S).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 2 , April 1969 , pp. 175 - 178
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Zariski, O. and Samuel, P., Commutative algebra, Vol. I. (D. Van Nostrand Company Inc., Princeton, New Jersey, 1958).Google Scholar