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
D. D. Anderson, editor. Factorization in integral domains, volume 189 of Lecture Notes in Pure and Applied Mathematics, New York, 1997. Marcel Dekker Inc.
H. Bass. On the ubiquity of Gorenstein rings. Math. Z., 82:8–28, 1963.
D. D. Anderson, D. F. Anderson, and M. Zafrullah. Factorization in integral domains. J. Pure Appl. Algebra, 69:1–19, 1990.
L. G. Chouinard, II Krull semigroups and divisor class groups. Canad. J. Math., 33:1459–1468, 1981.
E. G. Evans, Jr. Krull-Schmidt and cancellation over local rings. Pacific J. Math., 46:115–121, 1973.
A. Facchini. Module Theory. Endomorphism rings and direct sum decompositions in some classes of modules. Progress in Math. 167, Birkhauser Verlag, 1998.
A. Facchini. Direct sum decompositions of modules, semilocal endomorphism rings, and Krull monoids. J. Algebra, 256:280–307, 2002.
A. Facchini, and D. Herbera. Local Morphisms and Modules with a Semilocal Endomorphism Ring. Algebr. Represent. Theory, to appear.
A. Geroldinger. A structure theorem for sets of lengths. Colloq. Math., 78:225–259, 1998.
A. Geroldinger and F. Halter-Koch. Non-unique factorizations. Marcel Dekker, to appear.
F. Halter-Koch. Ideal Systems. An Introduction to Multiplicative Ideal Theory. Marcel Dekker, 1998.
W. Hassler, R. Karr, L. Klingler, and R. Wiegand. Indecomposable modules of large rank over Cohen-Macualay local rings. Trans. Amer. Math. Soc, to appear.
F. Kainrath. Factorization in Krull monoids with infinite class group. Colloq. Math., 80:23–30, 1999.
L. Klingler and L. S. Levy. Representation Type of Commutative Noetherian Rings I: Local Wildness. Pacific J. Math., 200:345–386, 2001.
L. Klingler and L. S. Levy. Representation Type of Commutative Noetherian Rings II: Local Tameness. Pacific J. Math., 200:387–483, 2001.
L. Klingler and L. S. Levy. Representation Type of Commutative Noetherian Rings III: Global Wildness and Tameness. Mem. Amer. Math. Soc., 832:1–170, 2005.
U. Krause. On monoids of finite real character. Proc. Amer. Math. Soc., 105:546–554, 1989.
L. S. Levy and C. J. Odenthal. Package deal theorems and splitting orders, in dimension 1. Trans. Amer. Math. Soc., 348:3457–3503, 1996.
E. Matlis. Some properties of Noetherian domains of dimension one. Canad. J. Math., 13:569–586, 1961.
E. Matlis. The minimal prime spectrum of a reduced ring. Illinois J. Math., 27:353–391, 1983.
M. E. Siddoway. On endomorphism rings of modules over Henselian rings. Comm. Algebra, 18:1323–1335, 1990.
P. Vámos. Decomposition problems for modules over valuation domains. J. London Math. Soc. (2), 41:10–26, 1990.
R. B. Warfield Jr. Cancellation of modules and groups and stable range of endomorphism rings. Pacific J. Math., 91:457–485, 1980.
R. Wiegand. Direct-sum decompositions over local rings. J. Algebra, 240: 83–97, 2001.
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
Facchini, A., Hassler, W., Klingler, L., Wiegand, R. (2006). Direct-sum decompositions over one-dimensional Cohen-Macaulay local 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_10
Download citation
DOI: https://doi.org/10.1007/978-0-387-36717-0_10
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)