Lectures on Exterior Algebras Over Commutative Rings |
Contents
3 Some Applications of the Multiplicative Structure of Exterior Algebras | 2-12 |
4 Localization of Rings | 2-18 |
5 Localization of Modules | 2-23 |
Copyright | |
11 other sections not shown
Common terms and phrases
apply bilinear Chapter commutative ring Conversely deduce defined example exterior algebra exterior powers exterior rank finitely generated coherent finitely generated R-module FR(S free module free presentation given hence Hom₂ induces injective integers integral domain isomorphism Jacobson radical ker f last Proposition last Theorem Let f linear m-dependence condition linear mapping local ring locally finitely locally free M/I M M₁ M₂ mapping f mapping g mapping of R-algebras mapping of R-modules maximal ideal minimal number module admitting determinants monomial multiplication n-linear n-multilinear map Nakayama's Lemma number of elements prime ideal Projective Modules Proof proves quotient R/det R/I M rankg rankR res rank result ring and let satisfies the linear short exact sequence submodule subset surjective tensor product universal property V/ker f W/cok f ΛΕ Λη Μ ΣΩ χε Μ