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

My PhD research concerned the Hopf-Galois module structure of rings of algebraic integers in tamely ramified extensions of local or global fields, and I continue to work on this topic. I also study the structure and properties of Hopf algebras that give Hopf-Galois structures on extensions of fields, and how these properties might be useful in answering questions of integral module structure.

I maintain an archive of the talks given at the annual conference Hopf algebras and Galois module theory.

I am interested in hearing from potential PhD students in Algebraic Number Theory.

Selected Publications

  • Truman PJ, Koch A, Kohl T, Underwood R. 2018. Isomorphism problems for Hopf-Galois structures on separable field extensions. Journal of Pure and Applied Algebra. doi> full text>
  • Truman PJ. 2018. Commutative Hopf-Galois module structure of tame extensions. Journal of Algebra. doi> link> full text>
  • Truman PJ. 2017. Commuting Hopf-Galois structures on a separable extension. Communications in Algebra, vol. 46(4), 1420-1427. doi> link> full text>
  • Truman PJ. 2016. Canonical Nonclassical Hopf–Galois Module Structure of Nonabelian Galois Extensions. Communications in Algebra, vol. 44(3), 1119-1130. doi> link> full text>
  • 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> full text>

Full Publications List show

Journal Articles

  • Truman PJ, Koch A, Kohl T, Underwood R. 2018. Isomorphism problems for Hopf-Galois structures on separable field extensions. Journal of Pure and Applied Algebra. doi> full text>
  • Truman PJ. 2018. Commutative Hopf-Galois module structure of tame extensions. Journal of Algebra. doi> link> full text>
  • Truman PJ. 2017. Commuting Hopf-Galois structures on a separable extension. Communications in Algebra, vol. 46(4), 1420-1427. doi> link> full text>
  • Truman PJ. 2016. Canonical Nonclassical Hopf–Galois Module Structure of Nonabelian Galois Extensions. Communications in Algebra, vol. 44(3), 1119-1130. doi> link> full text>
  • 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> full text>
  • Truman PJ. 2013. Integral Hopf-Galois structures for tame extensions. New York Journal of Mathematics, vol. 19, 647-655. full text>
  • Truman PJ. 2012. Hopf-Galois module structure of tame biquadratic extensions. Journal de Theorie des Nombres de Bordeaux, vol. 24(1), 173-199. full text>
  • Truman PJ. 2011. Towards a generalisation of Noether's theorem to nonclassical Hopf-Galois structures. New York Journal of Mathematics, vol. 17, 799-810. full text>
  • Truman PJ, Kohl T, Koch A, Underwood R. Normality and Short Exact Sequences of Hopf-Galois Structures. Communications in Algebra. full text>

Chapters

  • Truman PJ, Koch A, Kohl T, Underwood R. The Structure of Hopf Algebras Acting on Dihedral Extensions. In Advances in Algebra: Research from the Southern Regional Algebra Conference 2017. Springer. full text>

MAT-30022: Number Theory
MAT-30027: Codes and Cryptography
MAT-40008 Algebraic Number Theory