This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arapović, Miroslav, Characterization of the 0-diniensional rings, Glaanik Mat. 18 (1983), 39–46.
Arapović, Miroslav, The minimal 0-dimensional overrings of commutative rings, ibid., 47–52.
Arapović, Miroslav, On the embedding of a commutative ring into a 0-dimensional ring, ibid., 53–59.
Clifford, Alfred H. and Gordon B. Preston, Algebraic theory of semigroups, Volume 1, American Mathematical Society, 1961.
Coquand, Thierry, Henri Lombardi and Marie-Francoise Roy, An elementary characterization of Krull dimension, in From Sets and Types to Topology and Analysis, Oxford Logic Guides 48, Oxford University Press, 2005.
Fuchs, Laszlo and Luigi Salce, Modules over nonnoetherian domains, AMS 2001.
Gilmer, Robert, A new criterion for embeddability in a zero-dimensional commutative ring. Lecture notes in pure and applied mathematics 220, Marcel Decker 2001, 223–229.
Gilmer, Robert, Background and preliminaries on zero-dimensional rings, in Zero-dimensional commutative rings, Lecture notes in pure and applied mathematics 171, Marcel Dekker 1995, 1–13.
Gilmer, Robert, Zero dimensionality and products of commutative rings, ibid. 15–25.
Gilmer, Robert, Zero-dimensional extension rings and subrings, ibid. 27–39.
Gilmer, Robert and William J. Heinzer, On the imbedding of a direct product into a zero-dimensional commutative ring, Proc. Amer. Math. Soc. 106 (1989), 631–637.
Gilmer, Robert and William J. Heinzer, Products of commutative rings and zero dimensionality, Trans. Amer. Math. Soc. 331 (1992), 663–680.
Gilmer, Robert and William J. Heinzer, Zero-dimensionality in commutative rings, Proc. Amer. Math. Soc, 115 (1992), 881–893.
Gilmer, Robert and William J. Heinzer, Imbeddability of a commutative ring in a finite-dimensional ring, Manuscripta Math. 84 (1994) 401–414.
Glaz, Sarah, Commutative coherent rings. Lecture notes in mathematics 1371, Springer, 1989.
Heinzer, William J., Dimensions of extension rings, in Zero-dimensional commutative rings. Lecture notes in pure and applied mathematics 171, Marcel Dekker 1995, 57–64.
Kerr, Jeanne Wald, The polynomial ring over a Goldie ring need not be Goldie, J. Algebra 134 (1990) 344–352.
Lombardi, Henri, Dimension de Krull, Nullstellensätze et évaluation dynamique, Math. Zeit., 242 (2002) 23–46.
Maroscia, Paolo, Sur les anneaux de dimension zero, Atti Accad. Naz. Lincei Rend. CI. Sci. Fis. Mat. Natur. 56 (1974), 451–459.
Olivier, Jean-Pierre, Anneaux absolument plats universels et épimorphismes a buts reduits, Séminaire d’Algèbre Pierre Samuel, Paris, 1967–68.
Roitman, Moshe, On polynomial extensions of Mori domains over countable fields, J. Pure Appl. Alg. 64 (1990) 315–328
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer Science+Business Media, LLC
About this paper
Cite this paper
Brewer, J., Richman, F. (2006). Subrings of zero-dimensional rings. In: Brewer, J.W., Glaz, S., Heinzer, W.J., Olberding, B.M. (eds) Multiplicative Ideal Theory in Commutative Algebra. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-36717-0_5
Download citation
DOI: https://doi.org/10.1007/978-0-387-36717-0_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-24600-0
Online ISBN: 978-0-387-36717-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)