We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Characterization of lower quasi-modular extensions.
- Authors
Fliouet, El Hassane
- Abstract
Let K/k be a purely inseparable extension of characteristic p > 0 and of finite size. We recall that K/k is modular if for every n ∊ N, Kpn and k are k ∩ Kpn-linearly disjoint. A natural generalization of this notion is to say that K/k is lq-modular if K is modular over a finite extension of k. Our main objective is to extend in definite form some results and definitions of the lq-modularity that have already been obtained in the case limited by the finiteness condition imposed on [k : kp] in a rather general framework (framework of extensions of finite size called also q-finite extensions). First, by means of invariants, we characterize the lq-modularity of a q-finite extension. Moreover, we give a necessary and sufficient condition for K/k to be lq-modular. As a consequence, the lq-modularity is stable up to a finite extension of the choice of the ground field. This makes it possible to reduce the study of lq-modularity to the case of relatively perfect extensions.
- Subjects
INVARIANTS (Mathematics); RING extensions (Algebra)
- Publication
Palestine Journal of Mathematics, 2018, Vol 7, p125
- ISSN
2219-5688
- Publication type
Article