## Lattices over orders ii |

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### Contents

Norm and trace III 14 | 137 |

k The enveloping algebra III 20 | 143 |

Separable algebras III 27 | 150 |

Copyright | |

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### Common terms and phrases

A-fleld A-lattlces abelian group algebraic number field assume automorphism Bass-order Coker commutative diagram completely primary composition series containing Corollaryi decomposes decomposition Dedeklnd domain define denote direct sum domain with quotient elements epimorphism eplmorphlsm equivalence exact rows exact sequence exists finite dimensional K-algebra finite group finite type functor Hence hereditary R-order homomorphism homomorphlsm Horn Implies Indecomposable induces Infinite primes Integral Irreducible K-algebra Krull-Schmidt theorem Krull-Schmldt theorem lattices ldempotents left R-module Lemmai Let Math matrix maximal ideal maximal R-order modules monic Moreover morphism multiplication Nakayama's lemma natural isomorphism noetherian non-lsomorphlc notation ob(C polynomial prime ideal primitive principal ideal principal ideal domain progenerator proof quotient field Remarki representations resp separable K-algebra simple left skewfleld splitting field submodule suffices to show two-sided ideal