## Methods in Module TheoryA collection of articles embodying the work presented at the 1991 Methods in Module Theory Conference at the University of Colorado at Colorado Springs - facilitating the explanation and cross-fertilization of new techniques that were developed to answer a variety of module-theoretic questions. |

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### Contents

Left Almost Serial Rings and the Cartan Determinant Conjecture | 19 |

A Cotilting Theorem for Rings | 33 |

Examples of Reflexive Modules | 67 |

Category Equivalences Induced by Hom and Tensor Functors | 87 |

A Note on Proper Classes of Exact Sequences | 107 |

A Characterization of DedekindLike Orders that Are Bass | 135 |

A Survey | 149 |

Some New KTheoretic Invariants for Commutative Rings | 175 |

DirectSum Cancellation and Genus Class Groups | 203 |

Orders in Block Matrix Rings | 219 |

Colorings of Planar Maps and Residues of 1Forms | 237 |

Examples of NonFinitely Generated Projective Modules | 271 |

Gradability of Algebras | 285 |

A Change of Rings for Finitistic Dimension | 303 |

### Common terms and phrases

abelian group algebra apply artinian assume bimodules called cancellation claim closed commutative complete condition conjecture Consequently consider construction contains Corollary corresponding Dedekind domain defined definition denote Department of Mathematics determinant dimension direct sum domain element equal equivalent exact sequence example exists fact field finite follows function functor genus give given graph groups hence holds ideal idempotent implies indecomposable induced injective integers isomorphism lattice left module Lemma length locally Math matrix maximal ideal modules natural noetherian nonzero Note objects obtain particular prime projective Proof Proposition prove quotient R-module radical rank regular relations representations result right R-module ring satisfies serial rings simple space stable subgroup submodule summand Suppose Theorem theory torsion torsion-free unique uniserial University weakly