## Abelian Groups, Rings, Modules, and Homological AlgebraAbout the book... In honor of Edgar Enochs and his venerable contributions to a broad range of topics in Algebra, top researchers from around the world gathered at Auburn University to report on their latest work and exchange ideas on some of today's foremost research topics. This carefully edited volume presents the refereed papers of the participants of these talks along with contributions from other veteran researchers who were unable to attend. These papers reflect many of the current topics in Abelian Groups, Commutative Algebra, Commutative Rings, Group Theory, Homological Algebra, Lie Algebras, and Module Theory. Accessible even to beginning mathematicians, many of these articles suggest problems and programs for future study. This volume is an outstanding addition to the literature and a valuable handbook for beginning as well as seasoned researchers in Algebra. about the editors... H. PAT GOETERS completed his undergraduate studies in mathematics and computer science at Southern Connecticut State University and received his Ph.D. in 1984 from the University of Connecticut under the supervision of William J. Wickless. After spending one year in a post-doctoral position in Wesleyan University under the tutelage of James D. Reid, Goeters was invited for a tenure track position in Auburn University by Ulrich F. Albrecht. Soon afterwards, William Ullery and Overtoun Jenda were hired, and so began a lively Algebra group. OVERTOUN M. G. JENDA received his bachelor's degree in Mathematics from Chancellor College, the University of Malawi. He moved to the U.S. 1977 to pursue graduate studies at University of Kentucky, earning his Ph.D. in 1981 under the supervision of Professor Edgar Enochs. He then returned to Chancellor College, where he was a lecturer (assistant professor) for three years. He moved to the University of Botswana for another three-year stint as a lecturer before moving back to the University of Kentucky as a visiting assistant professor in 1987. In 1988, he joined the Algebra research group at Auburn University. |

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### Contents

LXXI | 140 |

LXXII | 141 |

147 | |

LXXIV | 148 |

LXXV | 149 |

LXXVI | 150 |

LXXVII | 153 |

LXXVIII | 155 |

XV | 16 |

XVI | 19 |

XVII | 20 |

23 | |

XIX | 24 |

29 | |

XXI | 30 |

XXII | 34 |

39 | |

XXIV | 40 |

XXV | 42 |

XXVI | 43 |

XXVII | 44 |

XXVIII | 46 |

XXIX | 49 |

51 | |

XXXI | 52 |

XXXII | 53 |

XXXIII | 56 |

59 | |

XXXV | 60 |

67 | |

XXXVII | 68 |

XXXVIII | 70 |

75 | |

XL | 76 |

XLI | 77 |

XLII | 79 |

XLIV | 80 |

XLV | 82 |

XLVII | 84 |

XLVIII | 85 |

XLIX | 86 |

87 | |

LI | 92 |

LII | 94 |

LIII | 95 |

LIV | 96 |

LV | 97 |

LVI | 98 |

LVII | 101 |

LVIII | 103 |

107 | |

LX | 109 |

LXI | 110 |

LXII | 113 |

LXIII | 116 |

121 | |

LXV | 122 |

LXVI | 123 |

LXVII | 128 |

LXVIII | 133 |

LXIX | 134 |

LXX | 138 |

159 | |

LXXX | 161 |

LXXXI | 162 |

LXXXII | 164 |

LXXXIII | 167 |

LXXXIV | 170 |

175 | |

LXXXVI | 176 |

LXXXVII | 180 |

183 | |

LXXXIX | 186 |

XC | 189 |

XCI | 194 |

XCII | 196 |

203 | |

XCIV | 204 |

XCV | 208 |

XCVI | 210 |

XCVII | 215 |

217 | |

XCIX | 218 |

C | 226 |

CI | 228 |

235 | |

CIII | 236 |

CIV | 237 |

CV | 239 |

CVI | 241 |

CVII | 243 |

CVIII | 244 |

CIX | 247 |

251 | |

CXI | 252 |

CXII | 258 |

CXIII | 260 |

265 | |

CXV | 266 |

CXVII | 270 |

CXVIII | 271 |

275 | |

CXXI | 276 |

CXXII | 277 |

CXXIII | 280 |

285 | |

CXXV | 286 |

CXXVI | 291 |

295 | |

CXXVIII | 296 |

CXXIX | 300 |

CXXX | 305 |

CXXXI | 309 |

315 | |

### Other editions - View all

Abelian Groups, Rings, Modules, and Homological Algebra Pat Goeters,Overtoun M.G. Jenda Limited preview - 2016 |

### Common terms and phrases

abelian groups Amer artinian assume co-local subgroup Cohen-Macaulay cohomology commutative ring compressible contains Corollary decomposition Dedekind-like ring define denote Department of Mathematics Derg direct sum direct summand element emod End(A endomorphism ring example exists F-separated cover finite rank finitely generated module flat covers flat right module following are equivalent fractional ideal functor G-Plex group G hence Hom(G homomorphism implies indecomposable injective hull injective modules injective resolution integral domain irreducible submodules isomorphic ker(G kernel Krull dimension Lemma local cohomology locally finite M-spaces Math Matlis maximal ideal monoform monomorphism noetherian ring non-zero submodule nonsingular Overtoun Jenda perfect domains positive integer Priifer domain prime ideal prime module projective Proposition prove pure subgroup quasilocal R-module r.cot.D resp result right ideal self-small subalgebra submodule of Q subring Suppose surjective Theorem topology torsion unique University of Kentucky valuation domain Warfield

### Popular passages

Page 217 - Throughout this paper, all rings are associative with identity and all modules are unitary.

Page 15 - An integral domain R is atomic if each nonzero nonunit of R is a product of irreducible elements (atoms) of R.

Page 23 - Л, with quotient field K, is called a pseudo-valuation domain (PVD) in case each prime ideal P of R is strongly prime, in the sense that xy € P,z £ K,y £ К implies that either x € P or ye P.