# Endomorphism algebras over large domains

Fundamenta Mathematicae (1998)

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

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topGöbel, 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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- [2] C. C. Chang and H. J. Keisler, Model Theory, Stud. Logic Found. Math. 73, North-Holland, 1990.
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- [5] P. C. Eklof and A. H. Mekler, Almost Free Modules, North-Holland, 1990. Zbl0718.20027
- [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] R. Göbel and W. May, Independence in completions and endomorphism algebras, Forum Math. 1 (1989), 215-226. Zbl0691.13004
- [8] R. Göbel and S. Shelah, Modules over arbitrary domains II, Fund. Math. 126 (1986), 217-243. Zbl0615.16021
- [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. Zbl0172.04801
- [12] M. Ziegler, Model theory of modules, Ann. Pure Appl. Logic 26 (1984), 149-213. Zbl0593.16019

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