Abstract
In this paper we study the structure of Zariski central rings with regular center i.p. biregular rings, and we obtain structure theorems for algebras which are finitely generated over their regular center, etc. Characterizations of certain classes of rings are being obtained by using localization at prime ideals and local-global theorems.
Similar content being viewed by others
References
E. P. Armendariz,On semiprime P.I. algebras over commutative regular rings, Pacific J. Math.66 (1976), 23–28.
E. P. Armendariz and J. W. Fisher,Regular P.I.-Rings, Proc. Amer. Math. Soc.39 (1973), 247–251.
E. P. Armendariz, J. W. Fisher and S. A. Steinberg,Central localizations of regular rings, Proc. Amer. Math. Soc.46 (1974), 315–321.
C. Faith,Algebra: Rings, Modules and Categories I, Springer-Verlag, Berlin-Heidelberg-New York, 1973.
J. W. Fisher,Von Neumann regular rings versus V-rings, inRing Theory, Proc. Univ. of Oklahoma Conference, M. Dekker Inc., New York, 1974, pp. 101–119.
J. W. Fisher and R. L. Snider,On the Von Neumann regularity of rings with regular prime factor rings, Pacific J. Math.54 (1974), 135–144.
O. Goldman,Rings and modules of quotients, J. Algebra13 (1969), 10–47.
J. Lambek and G. Michler,The torsion theory at a prime ideal of a right Noetherian rings, J. Algebra25 (1973), 364–389.
G. O. Michler and O. E. Villamayor,On rings whose simple modules are injective, J. Algebra25 (1973), 185–201.
B. Mueller,Localization of Non-commutative Noetherian Rings at Semiprime Ideals, Lecture Notes, McMaster University, 1974.
D. C. Murdoch and F. Van Oystaeyen,Noncommutative localization and sheaves, J. Algebra35 (1975), 500–515.
B. Osofsky,On twisted polynomial rings, J. Algebra18 (1971), 597–607.
C. Procesi,Rings with polynomial identities, inPure and Applied Math., Vol. 17, M. Dekker Inc. New York, 1973.
J. C. Robson and L. Small,Idempotent ideals in P.I. rings, J. London Math. Soc.14 (1976), 120–122.
J. Van Geel and F. Van Oystaeyen,Local-global results for regular rings, Comm. Algebra4 (1976), 811–821.
F. Van Oystaeyen,Prime Spectra in Non-commutative Algebra, Lecture Notes in Math.444, Springer-Verlag, Berlin-Heidelberg-New York, 1975.
F. Van Oystaeyen,Zariski central rings, Comm. Algebra6 (1978), 799–821.
F. Van Oystaeyen,Birational ring homomorphisms and ring extensions, inRing Theory, Proc. 1977 Conference, Lecture Notes, Vol. 40, M. Dekker Inc., New York, 1978, pp. 155–179.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nauwelaerts, E., Van Oystaeyen, F. Zariski extensions and biregular rings. Israel J. Math. 37, 315–326 (1980). https://doi.org/10.1007/BF02788929
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02788929