Shapiro's lemma

In mathematics, especially in the areas of abstract algebra dealing with group cohomology or relative homological algebra, Shapiro's lemma, also known as the Eckmann–Shapiro lemma, relates extensions of modules over one ring to extensions over another, especially the group ring of a group and of a subgroup. It thus relates the group cohomology with respect to a group to the cohomology with respect to a subgroup. Shapiro's lemma is named after Arnold S. Shapiro, who proved it in 1961;[1] however, Beno Eckmann had discovered it earlier, in 1953.[2]

  1. ^ Kolchin, Ellis Robert (1973), Differential algebra and algebraic groups, Pure and applied mathematics, vol. 54, Academic Press, p. 53, ISBN 978-0-12-417650-8.
  2. ^ Monod, Nicolas (2001), "Cohomological techniques", Continuous Bounded Cohomology of Locally Compact Groups, Lectures Notes in Mathematics, vol. 1758, Springer-Verlag, pp. 129–168, doi:10.1007/3-540-44962-0_5, ISBN 978-3-540-42054-5.