Journal of Commutative Algebra

Differential operators on modular extensions

Matthew Wechter

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Given a finite purely inseparable extension of positive characteristic, this paper determines necessary and sufficient conditions on the ring of relative differential operators to establish whether the extension is modular.

Article information

J. Commut. Algebra, Volume 7, Number 3 (2015), 447-458.

First available in Project Euclid: 14 December 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 12F15: Inseparable extensions 13N10: Rings of differential operators and their modules [See also 16S32, 32C38]

Modular purely inseparable differential operators divided powers positive characteristic


Wechter, Matthew. Differential operators on modular extensions. J. Commut. Algebra 7 (2015), no. 3, 447--458. doi:10.1216/JCA-2015-7-3-447.

Export citation


  • Roger C. Alperin, $p$-adic binomial coefficients $\mbox{\rm mod\,} p$, Amer. Math. Month. 92 (1985), 576–578.
  • Stephen U. Chase, Infinitesimal group scheme actions on finite field extensions, Amer. J. Math. 98 (1976), 441–480.
  • Murray Gerstenhaber, The fundamental form of an inseparable extension, Trans. Amer. Math. Soc. 227 (1977), 165–184.
  • A Grothendieck, Elements de geometrie algebrique iv, Publ. Math. IHES 20 (1964), 1965.
  • H. Hasse and F.K. Schmidt, Noch eine begrndung der theorie der hheren differentialquotienten in einem algebraischen funktionenkrper einer unbestimmten (nach einer brie ichen mitteilung von F.K. Schmidt in jena), J. reine angew. Math. 177 (1937), 215–223.
  • Nathan Jacobson, Lectures in abstract algebra, III, Springer-Verlag, New York, 1975; Theory of fields and Galois theory, Second corrected printing, Grad. Texts Math. 32, Springer-Verlag, New York.
  • Yoshikazu Nakai, High order derivations, I, Osaka J. Math. 7 (1970), 1–27.
  • Günter Pickert, Eine Normalform für endliche reininseparable Körpererweiterungen, Math. Z. 53 (1950), 133–135.
  • Richard Rasala, Inseparable splitting theory, Trans. Amer. Math. Soc. 162 (1971), 411–448.
  • Moss Eisenberg Sweedler, Structure of inseparable extensions, Ann. Math. 87 (1968), 401–410.