Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-05-19T02:19:51.607Z Has data issue: false hasContentIssue false

Upper Bounds on Homological Dimensions

Published online by Cambridge University Press:  22 January 2016

B. L. Osofsky*
Affiliation:
Institute for Advanced Study and Rutgers, The State University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The homological dimension of a module MR is often related to the cardinality of a set of generators for M or for right ideals of R. In this note, upper bounds for this homological dimension are obtained in two situations.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

[1] Auslander, M.: On the dimension of modules and algebras, III, Nagoya Math. J., 9 (1955), 6777.CrossRefGoogle Scholar
[2] Balcerzyk, S.: On projective dimension of direct limit of modules, Bull. Acad. Polon. Sci., Sér Sci. Math. Astron. Phys. 14 (1966), 241244.Google Scholar
[3] Berstein, I.: On the dimension of modules and algebras, IX, Nagoya Math. J., 13 (1958), 8384.CrossRefGoogle Scholar
[4] Bourbaki, N.: Algèbre commutative, Chap. 12, Paris, 1961.Google Scholar
[5] Eilenberg, S. and Steenrod, N.: Foundations of algebraic topology, Princeton, 1952.CrossRefGoogle Scholar
[6] Jategaonkar, A.V.: A counter-example in ring theory and homological algebra, Mimeographed notes, University of Rochester, 1967.Google Scholar
[7] Jensen, C.U.: On homological dimensions of rings with countably generated ideals, Math. Scand. 18 (1966), 97105.CrossRefGoogle Scholar
[8] Jensen, C.U.: Homological dimensions of ϰ-coherent rings, Math. Scand. 20 (1967), 5560.CrossRefGoogle Scholar
[9] Kaplansky, I.: Projective modules, Ann. of Math. 68 (1958), 372377.CrossRefGoogle Scholar
[10] Kaplansky, I.: Homological dimension of rings and modules, Mimeographed notes, University of Chicago, 1959.Google Scholar
[11] Lazard, D.: Sur les modules plats, Comp. Rend. 258 (1964), 63136316.Google Scholar
[12] Osofsky, B.L.: Global dimension of valuation rings, Trans. Amer. Math. Soc. 126 (1967), 136149.CrossRefGoogle Scholar
[13] Pierce, R.S.: The global dimension of boolean rings, to appear.Google Scholar
[14] Roos, J.E.: Sur les foncteurs dérivés de Applications., Comp. Rend. 252 (1961), 37023704.Google Scholar