Some model theory over hereditary noetherian domains

Journal of Algebra

Volumn 211, Issue 1, 1999, Pages 268-297

  Prest, Mike ^a   Puninski, Gennadi ^b  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b RUSSIAN STATE SOCIAL UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032622821     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1006/jabr.1998.7607     Document Type: Article

References (36)

1. Auslander M., Reiten I., Smalø S. O. Representation Theory of Artin Algebras. 1995;Cambridge Univ. Press, Cambridge.
2. Bavula V. Generalized Weyl algebras and their representations. Algebra i Analiz. 4:1992;75-97.
3. V. Bavula, The extension group Ext of the simple modules over the first Weyl algebra, 1997.
4. Bavula V., van Oystaeyen F. The simple modules of certain generalized crossed products. J. Algebra. 194:1997;521-566.
5. 2. Adv. Math. 39:1981;69-110.
6. Brenner S. Decomposition properties of some small diagrams of modules. Sympos. Math. 13:1974;127-141.
7. Eklof P. C., Fisher E. The elementary theory of abelian groups. Ann. Math. Logic. 4:1972;115-171.
8. Eklof P. C., Herzog I. Model theory of modules over a serial ring. Ann. Pure Appl. Math. 72:1995;145-176.
9. Eisenbud D., Robson J. C. Modules over Dedekind prime rings. J. Algebra. 16:1970;67-85.
10. Eisenbud D., Robson J. C. Hereditary noetherian prime rings. J. Algebra. 16:1970;86-104.
11. Faith C. Algebra: Rings, Modules and Categories. 1973;Springer-Verlag, Berlin/New York.
12. S. Garavaglia, Dimension and rank in the model theory of modules, University of Michigan, East Lansing, 1979.
13. Goodearl K. Von Neumann Regular Rings. 1979;Pitman, London.
14. Goodearl K. R., Boyle A. K. Dimension theory for nonsingular injective modules. Mem. Amer. Math. Soc. 177:1976.
15. Herzog I. Elementary duality for modules. Trans. Amer. Math. Soc. 340:1993;37-69.
16. Herzog I. The Auslander-Reiten translate. Contemp. Math. 130:1992;153-165.
17. Hodges W. A. Model Theory. 1993;Cambridge Univ. Press, Cambridge.
18. Jensen C. U., Lenzing H. Model Theoretic Algebra. 1989;Gordon and Breach, New York.
19. Kaplansky I. Infinite Abelian Groups. 1954;Univ. of Michigan Press, Ann Arbor.
20. Klingler L., Levy L. Wild torsion modules over Weyl algebras and general torsion modules over HNPs. J. Algebra. 172:1995;273-300.
21. Lenagan T. H. Bounded hereditary noetherian prime rings. J. London Math. Soc. 6:1973;241-246.
22. Marubayashi H. Modules over bounded Dedekind prime rings, II. Osaka J. Math. 9:1972;427-445.
23. McConnell J. C., Robson J. C. Homomorphisms and extensions of modules over certain differential polynomial rings. J. Algebra. 26:1973;319-342.
24. McConnell J. C., Robson J. C. Noncommutative Noetherian Rings. 1987;Wiley, New York.
25. Prest M. Model Theory and Modules. London Math. Soc. Lecture Note Ser. 130:1988;Cambridge Univ. Press, Cambridge.
26. Prest M. Remarks on elementary duality. Ann. Pure Appl. Logic. 62:1993;183-205.
27. M. Prest, Ziegler spectra of tame hereditary algebras, J. Algebra.
28. Puninski G. Superdecomposable pure-injective modules over commutative valuation rings. Algebra i Logika. 31:1992;655-671.
29. G. Puninski, Cantor-Bendixson rank of the Ziegler spectra over a commutative valuation domain, 1997.
30. G. Puninski, M. Prest, Ph. Rothmaler, Rings described by various purities, Comm. Algebra.
31. Ringel C. M. The Ziegler spectrum of a tame hereditary algebra. Colloq. Math. 76:1998;105-115.
32. Salce L. Valuation domains with superdecomposable pure injective modules. Lecture Notes Pure Appl. Math. 1993;Springer-Verlag, Berlin/New York. p. 241-245.
33. Szmielew W. Elementary properties of abelian groups. Fund. Math. 41:1955;203-271.
34. Ziegler M. Model theory of modules. Ann. Pure Appl. Logic. 26:1984;149-213.
35. Zimmermann W. Auslander-Reiten sequences over artinian rings. J. Algebra. 119:1988;366-392.
36. Zimmermann W. Auslander-Reiten sequences over derivation polynomial rings. J. Pure Appl. Algebra. 74:1991;317-332.