Geodesic
A Note on an Equivalence Relation on aPurely Inseparable Field Extension
Canadian mathematical bulletin, Tome 12 (1969) no. 2, pp. 175-178

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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 smallestnon-negative integer e such that and will be denoted bye (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). 
Rygg, P.; Lehman, B. A Note on an Equivalence Relation on aPurely Inseparable Field Extension. Canadian mathematical bulletin, Tome 12 (1969) no. 2, pp. 175-178. doi: 10.4153/CMB-1969-017-3
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     title = {A {Note} on an {Equivalence} {Relation} on {aPurely} {Inseparable} {Field} {Extension}},
     journal = {Canadian mathematical bulletin},
     pages = {175--178},
     year = {1969},
     volume = {12},
     number = {2},
     doi = {10.4153/CMB-1969-017-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-017-3/}
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