nLab quotient bimodule

Contents

Contents

Idea

The quotient of a bimodule by a subbimodule.

Definition

Given rings RR and SS, a RR-SS-bimodule BB, and a sub-RR-SS-bimodule II with a RR-SS-bimodule monomorphism i:IBi:I \hookrightarrow B, the quotient of BB by II is the initial RR-SS-bimodule B/IB/I with a RR-SS-bimodule homomorphism h:BB/Ih:B \to B/I such that for every element aIa \in I, h(i(a))=0h(i(a)) = 0: for any other RR-SS-bimodule AA with a RR-SS-bimodule homomorphism k:BAk:B \to A such that for every element aIa \in I, k(i(a))=0 Ak(i(a)) = 0_A, there is a unique RR-SS-bimodule homomorphism l:B/IAl:B/I \to A such that lh=kl \circ h = k.

Last revised on May 26, 2022 at 14:23:09. See the history of this page for a list of all contributions to it.