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THE ZIEGLER SPECTRUM OF THE RING OF ENTIRE COMPLEX VALUED FUNCTIONS

Published online by Cambridge University Press:  14 March 2019

SONIA L’INNOCENTE ,
FRANÇOISE POINT ,
GENA PUNINSKI  and
CARLO TOFFALORI
SONIA L’INNOCENTE
Affiliation:
DIVISION OF MATHEMATICS SCHOOL OF SCIENCE AND TECHNOLOGIES UNIVERSITY OF CAMERINO VIA MADONNA DELLE CARCERI9, 62032 CAMERINO, ITALYE-mail: [email protected]
FRANÇOISE POINT
Affiliation:
DEPARTMENT OF MATHEMATICS (LE PENTAGONE) UNIVERSITY OF MONS 20 PLACE DU PARC, B-7000 MONS, BELGIUME-mail: [email protected]
GENA PUNINSKI
Affiliation:
FACULTY OF MECHANICS AND MATHEMATICS BELARUSIAN STATE UNIVERSITY AV. NEZALEZHNOSTI4, MINSK 220030, BELARUS
CARLO TOFFALORI
Affiliation:
DIVISION OF MATHEMATICS SCHOOL OF SCIENCE AND TECHNOLOGIES UNIVERSITY OF CAMERINO VIA MADONNA DELLE CARCERI 9, 62032 CAMERINO, ITALYE-mail: [email protected]
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Abstract

We will describe the Ziegler spectrum over the ring of entire complex valued functions.

Keywords

Primary 03C6003C2013C1130D20Ziegler spectrumentire functionsnonprincipal ultrafiltersBézout domains
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 1 , March 2019 , pp. 160 - 177
Copyright
Copyright © The Association for Symbolic Logic 2019 

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References

REFERENCES

Ahlfors, L. W., Complex Analysis, McGraw-Hill, 1979.Google Scholar
Chang, C. C. and Keisler, H. J., Model Theory, Studies in Logic and Foundations of Mathematics, vol. 73, North-Holland, 1973.Google Scholar
Fuchs, L. and Salce, L., Modules Over Non-Noetherian Domains, Mathematical Surveys and Monographs, vol. 84, American Mathematical Society, 2001.Google Scholar
Gillman, L. and Jerison, M., Rings of Continuous Functions, D. Van Nostrand, New York, 1960.10.1007/978-1-4615-7819-2CrossRefGoogle Scholar
Golasiński, M. and Henriksen, M., Residue class rings of real analytic functions. Colloquium Mathematicum, vol. 104 (2006), pp. 85–97.10.4064/cm104-1-5CrossRefGoogle Scholar
Gregory, L., Decidability for the theory of modules over valuation domains, this Journal, vol. 80 (2015), pp. 684–711.Google Scholar
Helmer, O., Divisibility properties of integral functions. Duke Mathematical Journal, vol. 6 (1940), pp. 345–356.10.1215/S0012-7094-40-00626-3CrossRefGoogle Scholar
Helmer, O., The elementary divisor theorem for certain rings without chain conditions. Bulletin of the American Mathematical Society, vol. 49 (1943), pp. 225–236.10.1090/S0002-9904-1943-07886-XCrossRefGoogle Scholar
Henriksen, M., On the prime ideals of the ring of entire functions. Pacific Journal of Mathematics, vol. 3 (1953), pp. 711–720.10.2140/pjm.1953.3.711CrossRefGoogle Scholar
Jech, T., Set Theory, Academic Press, 1978.Google Scholar
Jensen, C. U., La dimension globale de l’anneau des fonctions entières. Comptes Rendus Mathematique Academie des Sciences, Paris, vol. 294 (1982), pp. 385–386.Google Scholar
Jensen, C. U., Some curiosities of rings of analytic functions. Journal of Pure and Applied Algebra, vol. 38 (1985), pp. 277–283.10.1016/0022-4049(85)90014-3CrossRefGoogle Scholar
L’Innocente, S., Puninski, G., and Toffalori, C., On the decidability of the theory of modules over the ring of algebraic integers. Annals of Pure and Applied Logic, vol. 168 (2017), pp. 1507–1516.10.1016/j.apal.2017.02.003CrossRefGoogle Scholar
Matlis, E., 1-Dimensional Cohen-Macaulay Rings, Lecture Notes in Mathematics, vol. 327, Springer, 1973.Google Scholar
Prest, M., Purity, Spectra and Localization, Encyclopedia of Mathematics and its Applications, vol. 121, Cambridge University Press, 2009.10.1017/CBO9781139644242CrossRefGoogle Scholar
Puninski, G., Cantor–Bendixson rank of the Ziegler spectrum over a commutative valuation domain, this Journal, vol. 64 (1999), pp. 1512–1518.Google Scholar
Puninski, G., Serial Rings, Kluwer, 2001.10.1007/978-94-010-0652-1CrossRefGoogle Scholar
Puninski, G., Puninskaya, V., and Toffalori, C., Decidability of the theory of modules over commutative valuation domains. Annals of Pure and Applied Logic, vol. 145 (2007), pp. 258–275.10.1016/j.apal.2006.09.002CrossRefGoogle Scholar
Puninski, G. and Toffalori, C., Decidability of modules over a Bézout domain D + XQ[X] with D principal ideal domain and Q its field of fractions , this Journal, vol. 79 (2014), pp. 296–305.Google Scholar
Puninski, G. and Toffalori, C., Some model theory of modules over Bézout domains. The width. Journal of Pure and Applied Algebra, vol. 219 (2015), pp. 807–829.10.1016/j.jpaa.2014.04.031CrossRefGoogle Scholar
Rudin, W., Real and Complex Analysis, McGraw-Hill International Editions, 1987.Google Scholar
Saks, S. and Zygmund, A., Analytic Functions, Monografie matematyczne, Institut Matematyczny Polskiej Academii Nauk, vol. 28, Ukł. Polskiego Towarzystwa Matematycznego, 1952.Google Scholar
Ziegler, M., Model theory of modules. Annals of Pure and Applied Logic, vol. 26 (1984), pp. 149–213.10.1016/0168-0072(84)90014-9CrossRefGoogle Scholar
Zimmermann-Huisgen, B. and Zimmermann, W., Algebraically compact rings and modules. Mathematische Zeitschrift, vol. 161 (1978), pp. 81–93.10.1007/BF01175615CrossRefGoogle Scholar