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| Keywords: Module properties in commutative algebra.svg en Properties of modules in commutative algebras and implications between them References free > projective projective modules are exactly direct summands of free ones Lang III 4 p 137 projective > flat same reason tensor products commute with direct sums flat > torsion-free torsion is the kernel of M tensor A -> Q if Q is the total quotient ring M the module A the ring module torsion-free + ring Dedekind > module flat Liu Corollary 1 2 14 module flat and ring perfect > module projective wikipedia page for perfect rings module projective + ring local > module free Matsumura Theorem 2 5 module projective + ring PID > module free Lang Theorem III 7 1 p 146 and App 2 2 p 880 2012-04-10 own KonradVoelkel This work is inspired by a public domain work from German wikipedia cc-zero Uploaded with UploadWizard Commutative algebra Module theory | ||||
