Dr Paul Truman

Title: Lecturer
Phone: 01782 733246
Email: p.j.truman@keele.ac.uk
Location: MacKay Building Room 2.16
Role:
Contacting me:

As an undergraduate, I read for an MMath at the University of Oxford (Exeter College). I graduated in 2005 and moved to the University of Exeter where I studied for a PhD in algebraic number theory under the supervision of Nigel Byott. After submitting my thesis I held two short term posts in Exeter, initially as a research fellow and subsequently as a teaching fellow. I finally left Exeter in 2010 to come to Keele.

My research interests are in algebra and number theory, specifically the Galois module structure of algebraic integers. I am particularly interested in Hopf-Galois module theory, where a Hopf algebra takes the place of the Galois group. 

My PhD research concerned the Hopf-Galois module structure of tamely ramified extensions, and possible generalisations of Noether’s theorem to this setting. Since then, in addition to considering further generalisations of the results of my thesis, I have studied the application of these techniques to wildly ramified extensions. In particular, I am interested in the possibility of a Hopf-Galois analogue of Elder’s concept of Galois Scaffolding.

Selected Publications

  • Truman PJ. 2017. Commuting Hopf-Galois structures on a separable extension. Communications in Algebra. doi> link>
  • Truman PJ. 2016. Canonical Nonclassical Hopf–Galois Module Structure of Nonabelian Galois Extensions. Communications in Algebra, vol. 44(3), 1119-1130. doi> link>
  • Truman PJ. 2016. Hopf-Galois module structure of tame Cp×Cp extensions. Journal de Theorie des Nombres de Bordeaux, vol. 28(2), 557-582. doi>
  • Truman PJ. 2013. Integral Hopf-Galois structures for tame extensions. New York Journal of Mathematics, vol. 19, 647-655.
  • Truman PJ. 2012. Hopf-Galois module structure of tame biquadratic extensions. Journal de Theorie des Nombres de Bordeaux, vol. 24(1), 173-199.

Full Publications List show

Journal Articles

  • Truman PJ. 2017. Commuting Hopf-Galois structures on a separable extension. Communications in Algebra. doi> link>
  • Truman PJ. 2016. Canonical Nonclassical Hopf–Galois Module Structure of Nonabelian Galois Extensions. Communications in Algebra, vol. 44(3), 1119-1130. doi> link>
  • Truman PJ. 2016. Hopf-Galois module structure of tame Cp×Cp extensions. Journal de Theorie des Nombres de Bordeaux, vol. 28(2), 557-582. doi>
  • Truman PJ. 2013. Integral Hopf-Galois structures for tame extensions. New York Journal of Mathematics, vol. 19, 647-655.
  • Truman PJ. 2012. Hopf-Galois module structure of tame biquadratic extensions. Journal de Theorie des Nombres de Bordeaux, vol. 24(1), 173-199.
  • Truman PJ. 2011. Towards a generalisation of Noether's theorem to nonclassical Hopf-Galois structures. New York Journal of Mathematics, vol. 17, 799-810.

MAT-10038: Algebra I
MAT-10040: Algebra II
MAT-20004: Complex Variable I and Vector Calculus
MAT-20025: Abstract Algebra
MAT-30022: Number Theory
MAT-30027: Codes and Cryptography

First Year Tutor Team
SSLC Member