Fiting ideals Sample Clauses

Fiting ideals. ‌ In this subsection we recall the higher Fitting ideals of finitely generated modules over 𝑅. To do this we assume that 𝑀 is finitely generated and fix a presentation 𝑅𝑛 𝜙 𝑅𝑚 → 𝑀 → 0. We say that 𝑀 has a quadratic presentation if one can take 𝑛 = 𝑚 in such a pres−→entation. For any integer 𝑟 ≤ 𝑚 the map 𝜙 induces a pairing Φ𝑟 : 𝑚−𝑟 𝑅𝑛 ⊗ 𝑚−𝑟 𝑅𝑚,∗ → 𝑅, 𝑎 ⊗ 𝑏 ↦→ 𝑏 (( 𝑚−𝑟 𝜙)(𝑎))
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