Homotopy Type Theory bimodule > history (Rev #3, changes)

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Definiton

Let RR and SS be commutative ring s s. and A let M R M R - be a left R S R S -module -bimodule and is a an rightSSabelian group -module, with a left multiplicativebilinearBB with aRRtrilinear - multiplicative action $R$-$S$-biaction .α l:R×A→A\alpha_l:R \times A \to A and a right multiplicative bilinear SS-action α r:A×S→A\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 ℤ\mathbb{Z}-ℤ\mathbb{Z}-bimodule.
  • Every left RR-module is a RR-ℤ\mathbb{Z}-bimodule.
  • Every right RR-module is a ℤ\mathbb{Z}-RR-bimodule.

See also

Revision on May 25, 2022 at 03:24:19 by Anonymous?. See the history of this page for a list of all contributions to it.

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