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Part One Groups Rings and Modules
156 other sections not shown
abelian group additive algebraic apply associated assume automorphism basis called Chapter character characteristic clear closed coefficients complex conclude consider consisting contained Corollary cyclic define definition denote derivation determined diagram dimension direct sum element embedding equal exact sequence Example exercise exists expression extension fact factor field finite fixed follows function functor Furthermore Galois given gives Hence homomorphism ideal independent induced injective integer inverse irreducible isomorphism lemma Let G linear map linearly matrix maximal means module morphism multiplicative normal object obtain obvious operation polynomial positive prime Proof Proposition prove reader relation representation resolution respect ring root satisfying separable sequence Show simple subgroup submodule subset Suppose symmetric Theorem trivial unique unit valuation variable vector space verified write zero