Endomorphism algebras over large domains

Rüdiger Göbel; Simone Pabst

Fundamenta Mathematicae (1998)

  • Volume: 156, Issue: 3, page 211-240
  • ISSN: 0016-2736

Abstract

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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

How to cite

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Göbel, Rüdiger, and Pabst, Simone. "Endomorphism algebras over large domains." Fundamenta Mathematicae 156.3 (1998): 211-240. <http://eudml.org/doc/212270>.

@article{Göbel1998,
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},
author = {Göbel, Rüdiger, Pabst, Simone},
journal = {Fundamenta Mathematicae},
keywords = {endomorphism algebras; realizations of algebras},
language = {eng},
number = {3},
pages = {211-240},
title = {Endomorphism algebras over large domains},
url = {http://eudml.org/doc/212270},
volume = {156},
year = {1998},
}

TY - JOUR
AU - Göbel, Rüdiger
AU - Pabst, Simone
TI - Endomorphism algebras over large domains
JO - Fundamenta Mathematicae
PY - 1998
VL - 156
IS - 3
SP - 211
EP - 240
AB - 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
LA - eng
KW - endomorphism algebras; realizations of algebras
UR - http://eudml.org/doc/212270
ER -

References

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  1. [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. Zbl0808.16030
  2. [2] C. C. Chang and H. J. Keisler, Model Theory, Stud. Logic Found. Math. 73, North-Holland, 1990. 
  3. [3] A. L. S. Corner and R. Göbel, Prescribing endomorphism algebras - A unified treatment, Proc. London Math. Soc. (3) 50 (1985), 447-479. Zbl0562.20030
  4. [4] M. Dugas and R. Göbel, Every cotorsion-free algebra is an endomorphism algebra, Math. Z. 181 (1982), 451-470. Zbl0501.16031
  5. [5] P. C. Eklof and A. H. Mekler, Almost Free Modules, North-Holland, 1990. Zbl0718.20027
  6. [6] L. Fuchs and L. Salce, Modules over Valuation Domains, Lecture Notes in Pure and Appl. Math. 97, Marcel Dekker, New York, 1985. Zbl0578.13004
  7. [7] R. Göbel and W. May, Independence in completions and endomorphism algebras, Forum Math. 1 (1989), 215-226. Zbl0691.13004
  8. [8] R. Göbel and S. Shelah, Modules over arbitrary domains II, Fund. Math. 126 (1986), 217-243. Zbl0615.16021
  9. [9] S. Pabst, Kaplansky's Testprobleme in der Modultheorie über kommutativen Ringen, Dissertation, Universität/GHS Essen, 1994. 
  10. [10] M. Prest, Model Theory and Modules, London Math. Soc. Lecture Note Ser. 130, Cambridge Univ. Press, 1988. 
  11. [11] R. B. Warfield, Purity and algebraic compactness for modules, Pacific J. Math. 28 (1969), 699-719. Zbl0172.04801
  12. [12] M. Ziegler, Model theory of modules, Ann. Pure Appl. Logic 26 (1984), 149-213. Zbl0593.16019

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