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Elementary epimorphisms

Published online by Cambridge University Press:  12 March 2014

Philipp Rothmaler
Philipp Rothmaler*
Affiliation:
Department of Mathematics, The Ohio State University, 4240 Campus Drive, Lima, OH 45804, USA, E-mail: rothmaler.1@osu.edu
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Abstract

The concept of elementary epimorphism is introduced. Inverse systems of such maps are considered, and a dual of the elementary chain lemma is found (Cor. 4.2). The same is done for pure epimorphisms (Cor. 4.3 and 4.4). Finally, this is applied to certain inverse limits of flat modules (Thm. 6.4) and certain inverse limits of absolutely pure modules (Cor. 6.3).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 2 , June 2005 , pp. 473 - 487
Copyright
Copyright © Association for Symbolic Logic 2005

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References

REFERENCES

[1] Chang, C. C. and Keisler, H. J., Model theory, Studies in Logic and the Foundation of Mathematics, vol. 73, North-Holland, Amsterdam, 1973.Google Scholar
[2] Fisher, E. R., Abelian structures I, Abelian group theory, Proceedings of the 2nd New Mexico State University conference, 1976, Lecture Notes in Mathematics, vol. 616, Springer, Berlin, 1977, pp. 270–322.Google Scholar
[3] Fuchs, L., Infinite abelian groups, Academic Press, New York, 1970.Google Scholar
[4] Gratzer, G., Universal algebra, Springer, New York, 1979.Google Scholar
[5] Henkin, L., A problem on inverse mapping systems, Proceedings of the American Mathematical Society, vol. 1 (1950), pp. 224–225.CrossRefGoogle Scholar
[6] Herzog, I., Elementary duality of modules, Transactions of the American Mathematical Society, vol. 340 (1993), no. 1, pp. 37–69.Google Scholar
[7] Hodges, W., Model theory, Encyclopedia of Mathematics and its Applications, vol. 42, Cambridge University Press, Cambridge, 1993.Google Scholar
[8] Laradji, A., Inverse limits of algebras as retracts of their direct products, Proceedings of the American Mathematical Society, vol. 131 (2003), no. 4, pp. 1007–1010.CrossRefGoogle Scholar
[9] Mal'tsev, A. I., Algebraic systems, Grundlehren der mathematischen Wissenschaften, vol. 192, Springer, Berlin, 1973.Google Scholar
[10] Prest, M., Model theory and modules, London Mathematical Society Lecture Notes Series, vol. 130, Cambridge University Press, Cambridge, 1988.CrossRefGoogle Scholar
[11] Prest, M., Remarks on elementary duality, Annals of Pure and Applied Logic, vol. 62 (1993), pp. 183–205.Google Scholar
[12] Prest, M., Rothmaler, Ph., and Ziegler, M., Absolutely pure and flat modules and ‘indiscrete’ rings, Journal of Algebra, vol. 174 (1995), pp. 349–372.Google Scholar
[13] Rothmaler, Ph., Purity in model theory, Proceedings of the conference on model theory and algebra, Essen/Dresden, 1994/95 (Droste, M. and GÖbel, R., editors), Algebra, Logic and Application Series, vol. 9, Gordon & Breach, 1997, pp. 445–469.Google Scholar
[14] Rothmaler, Ph., Introduction to model theory, Algebra, Logic and Application Series, Gordon & Breach, 2000.Google Scholar
[15] Sacerdote, G. S., Elementary properties of free groups, Transactions of the American Mathematical Society, vol. 178 (1973), pp. 127–138.Google Scholar
[16] Sacerdote, G. S., Infinite coforcing in model theory, Advances in Mathematics, vol. 17 (1975), pp. 261–280.Google Scholar
[17] Waterhouse, W. C., An empty inverse limit, Proceedings of the American Mathematical Society, vol. 36 (1972), p. 618.Google Scholar
[18] Wisbauer, R., Foundations of module and ring theory, Gordon and Breach, Philadelphia, 1991.Google Scholar