tensor product of modules
type: Thing
description: operation that pairs a left and a right 𝑅‐module into an abelian group
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  value: \begin{aligned}M\otimes_RN&=(M\otimes_{\mathbb Z}N)/I\\I&=(m\otimes_{\mathbb Z}rn-mr\otimes_{\mathbb Z}n\colon m\in M,\,n\in N,\;r\in R)\end{aligned}
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    value: \begin{aligned}M\otimes_RN&=(M\otimes_{\mathbb Z}N)/I\\I&=(m\otimes_{\mathbb Z}rn-mr\otimes_{\mathbb Z}n\colon m\in M,\,n\in N,\;r\in R)\end{aligned}
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citations:
  source: OpenAlex
  stated in qid: Q107507571
  retrieved: 2022-01-26
citations:
  source: Freebase Data Dumps
  stated in qid: Q15241312
  pub year: 2013
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  domain: binary_operation
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  api version: v1
  served at: 2026-08-24T21:41:05.752006Z
  entity updated at: 2026-05-03T23:45:09.469384+00:00Z
  entity created at: 2026-04-10T23:36:46.391084+00:00Z