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A Note on an Equivalence Relation on aPurely Inseparable Field Extension
Published online by Cambridge University Press: 20 November 2018
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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).
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- Copyright © Canadian Mathematical Society 1969
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