Review Note
Last Update: 10/25/2023 09:09 PM
Current Deck: Default::algebra::Advanced Algebra::lecture02 - quotient modules
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bilinear map of modules
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Let \(M,N,L\) be R-modules. A map \(M × N → L\) is bilinear if it is linear in both arguments, i.e.
i) \(φ(r_1m_1 + r_2m_2, n) = r_1φ(m_1,n) + r_2φ(m_2,n)\)
ii) \(φ(m,r_1n_1 + r_2n_2) = r_1φ(m,n_1) + r_2φ(m,n_2)\)
i) \(φ(r_1m_1 + r_2m_2, n) = r_1φ(m_1,n) + r_2φ(m_2,n)\)
ii) \(φ(m,r_1n_1 + r_2n_2) = r_1φ(m,n_1) + r_2φ(m,n_2)\)
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