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3 results

  • II - Foundations

  • Skip Garibaldi, Institute for Defense Analyses, USA, Holger P. Petersson, FernUniversität in Hagen, Michel L. Racine, University of Ottawa
  • Book:
    Albert Algebras over Commutative Rings
    Published online:
    07 November 2024
    Print publication:
    21 November 2024, pp 43-108

  • Summary

    This chapter starts out with a short introduction to the language of nonassociative algebras over commutative rings. It then proceeds to familiarize the reader with two of the most important elementary techniques utilized in this book: scalar extensions (also known as base change) and finitely generated projective modules. Standard properties of involutions and quadratic maps are also recalled before we conclude the chapter with a short introduction into Roby’s theory (1963) of polynomial laws.

  • Projective freeness and stable rank of algebras of complex-valued BV functions

  • Part of
  • Alexander Brudnyi
  • Journal:
    Canadian Mathematical Bulletin / Volume 66 / Issue 3 / September 2023
    Published online by Cambridge University Press:
    16 January 2023, pp. 844-853
    Print publication:
    September 2023
    • Article
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  • The paper investigates the algebraic properties of weakly inverse-closed complex Banach function algebras generated by functions of bounded variation on a finite interval. It is proved that such algebras have Bass stable rank 1 and are projective-free if they do not contain nontrivial idempotents. These properties are derived from a new result on the vanishing of the second Čech cohomology group of the polynomially convex hull of a continuum of a finite linear measure described by the classical H. Alexander theorem.

  • Appendix A - Algebra

  • Greg Friedman, Texas Christian University
  • Book:
    Singular Intersection Homology
    Published online:
    18 September 2020
    Print publication:
    24 September 2020, pp 713-738

  • Summary

    We review some algebraic topics that are useful throughout the text, including the Koszul sign convention, chain homotopies, algebraic mapping cones, projective modules, Dedekind domains, and signatures of bilinear forms.