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Let K be a purely inseparable extension of a field k of characteristic p ≠ 0. Suppose that is finite. We recall that K/k is lq-modular if K is modular over a finite extension of k. Moreover, there exists a smallest extension m/k (resp. M/K) such that K/m (resp. M/k) is lq-modular. Our main result states the existence of a greatest lq-modular and relatively perfect subextension of K/k. Other results can be summarized in the following:
1. The product of lq-modular extensions over k is lq-modular...
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