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Communications in Algebra Volume 36, 2008 - Issue 7
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Original Articles

Minimal Modules Over Serial Rings

Sonia L'innocente Department of Mathematics and Computer Science, University of Camerino, Camerino, Italy
,
Vera Puninskaya Department of Mathematics and Computer Science, University of Camerino, Camerino, Italy
&
Carlo Toffalori Department of Mathematics and Computer Science, University of Camerino, Camerino, ItalyCorrespondence[email protected]
Pages 2750-2763 | Received 12 Jul 2006, Published online: 20 Jun 2008

REFERENCES

  • Eklof , P. , Herzog , I. ( 1995 ). Model theory of modules over a serial ring . Ann. Pure Appl. Math. 72 : 145 – 176 .
  • Facchini , A. ( 1998 ). Module Theory . Birkhäuser .
  • Herzog , I. , Rothmaler , P. ( 1989 ). Modules with regular generic types I, II, III . In: Nesin , A. , Pillay , A. , eds. The Model Theory of Groups . Notre Dame Mathematical Lectures 11 . Notre Dame : University Press , pp. 138 – 176 .
  • Herzog , I. , Puninskaya , V. ( 1996 ). The model theory of divisible modules over a domain . Fund. Math. Appl. 2 : 563 – 594 .
  • Jensen , C. , Lenzing , H. ( 1989 ). Model Theoretic Algebra, with Particular Emphasis on Fields, Rings and Modules . Gordon and Breach .
  • Leonesi , S. , L'Innocente , S. , Toffalori , C. ( 2005 ). Weakly minimal modules over integral group rings and over related classes of rings . Math. Log. Quart. 51 : 613 – 625 .
  • L'Innocente , S. , Puninskaya , V. , Toffalori , C. ( 2005 ). Strongly minimal modules over group rings . Comm. Algebra 33 : 2089 – 2107 .
  • L'Innocente , S. , Puninskaya , V. , Toffalori , C. ( 2006 ). Minimalities and modules over Dedekind-like rings . Comm. Algebra 34 : 2453 – 2466 .
  • Loveys , J. ( 1983 ). On locally modular weakly minimal theories . Arch. Math. Logic 32 : 173 – 194 .
  • Loveys , J. ( 1990 ). Weakly minimal groups of unbounded exponent . J. Symbolic Logic 55 : 928 – 937 .
  • McConnell , J. C. , Robson , J. C. ( 2001 ). Noncommutative Noetherian Rings . American Mathematical Society .
  • Müller , B. ( 1992 ). The structure of serial rings . In: Methods in Module Theory . Marcel Dekker , pp. 249 – 270 .
  • Prest , M. ( 1988 ). Model Theory and Modules . Cambridge: Cambridge University Press .
  • Puninskaya , V. ( 1996 ). Strongly minimal modules over right distributive rings . Algebra and Logic 35 : 345 – 358 .
  • Puninskaya , V. ( 2003 ). Strongly minimal modules . J. Math. Sci. 114 : 1127 – 1157 .
  • Puninskaya , V. The model theory of divisible modules over ore domains . Unpublished notes .
  • Puninski , G. ( 2001 ). Serial Rings . Kluwer .
  • Puninski , G. , Wisbauer , R. ( 1996 ). Σ-injective modules over left duo and left distributive rings . J. Pure Applied Algebra 113 : 55 – 66 .
  • Ziegler , M. ( 1984 ). Model theory of modules . Ann. Pure Appl. Logic 26 : 149 – 213 .
  • Communicated by H. D. Macpherson.

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