Homotopy Type Theory bimodule > history (Rev #2)

Definiton

Let RR and SS be commutative rings and let MM be a left RR-module and a right SS-module, with a left multiplicative bilinear RR-action α l:R×AA\alpha_l:R \times A \to A and a right multiplicative bilinear SS-action α r:A×SA\alpha_r:A \times S \to A. MM is a RR-SS-bimodule if

p: m:M a:R b:Sα l(a,α r(m,b))=α r(α l(a,m),b)p: \prod_{m:M} \prod_{a:R} \prod_{b:S} \alpha_l(a, \alpha_r(m, b)) = \alpha_r(\alpha_l(a, m), b)

For a commutative ring RR, a RR-RR-bimodule is also called a RR-bimodule.

Properties

  • Every abelian group is a \mathbb{Z}-\mathbb{Z}-bimodule.
  • Every left RR-module is a RR-\mathbb{Z}-bimodule.
  • Every right RR-module is a \mathbb{Z}-RR-bimodule.

See also

Revision on May 25, 2022 at 01:01:14 by Anonymous?. See the history of this page for a list of all contributions to it.