ArticleOriginal scientific text

Title

Endomorphism algebras over large domains

Authors 1, 2

Affiliations

  1. achbereich 6, Universität Essen, 45117 Essen, Germany
  2. Dublin Institute of Technology, 30 Upper Pembroke Street, Dublin 2, Ireland

Abstract

The paper deals with realizations of R-algebras A as endomorphism algebras End G ≅ A of suitable R-modules G over a commutative ring R. We are mainly interested in the case of R having "many prime ideals", such as R = ℝ[x], the ring of real polynomials, or R a non-discrete valuation domain

Bibliography

  1. C. Böttinger and R.Göbel, Modules with two distinguished submodules, in: Proc. 1991 Curaçao Conf. Abelian Groups, Lecture Notes in Pure and Appl. Math. 146, Marcel Dekker, New York, 1993, 97-104.
  2. C. C. Chang and H. J. Keisler, Model Theory, Stud. Logic Found. Math. 73, North-Holland, 1990.
  3. A. L. S. Corner and R. Göbel, Prescribing endomorphism algebras - A unified treatment, Proc. London Math. Soc. (3) 50 (1985), 447-479.
  4. M. Dugas and R. Göbel, Every cotorsion-free algebra is an endomorphism algebra, Math. Z. 181 (1982), 451-470.
  5. P. C. Eklof and A. H. Mekler, Almost Free Modules, North-Holland, 1990.
  6. L. Fuchs and L. Salce, Modules over Valuation Domains, Lecture Notes in Pure and Appl. Math. 97, Marcel Dekker, New York, 1985.
  7. R. Göbel and W. May, Independence in completions and endomorphism algebras, Forum Math. 1 (1989), 215-226.
  8. R. Göbel and S. Shelah, Modules over arbitrary domains II, Fund. Math. 126 (1986), 217-243.
  9. S. Pabst, Kaplansky's Testprobleme in der Modultheorie über kommutativen Ringen, Dissertation, Universität/GHS Essen, 1994.
  10. M. Prest, Model Theory and Modules, London Math. Soc. Lecture Note Ser. 130, Cambridge Univ. Press, 1988.
  11. R. B. Warfield, Purity and algebraic compactness for modules, Pacific J. Math. 28 (1969), 699-719.
  12. M. Ziegler, Model theory of modules, Ann. Pure Appl. Logic 26 (1984), 149-213.
Pages:
211-240
Main language of publication
English
Received
1996-08-18
Accepted
1997-12-22
Published
1998
Exact and natural sciences