Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-26T11:36:46.331Z Has data issue: false hasContentIssue false

Projective modules over pullback rings

Published online by Cambridge University Press:  24 October 2008

A. N. Wiseman
Affiliation:
Department of Engineering Mathematics, LoughboroughUniversity of Technology

Extract

Given two homomorphisms of rings j1:R1R' and j2: R2R' we may construct a new ring R called the pullback of R1 and R2 over R', together with homomorphisms i1:RR1 and i2:RR2 such that j1i1= j2i2. There are many instances where special cases of pullbacks have been studied, either to construct new examples of rings or to reduce various problems to those concerning much simpler rings. A few of these instances are given in the references. Thus a general study of the properties of pullbacks in terms of those of the component rings would seem to be useful.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1985

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Carrig, J. E.. The homological dimensions of symmetric algebras. Trans. Amer. Math. Soc. 236 (1978), 275285.Google Scholar
[2]Dobbs, D. E.. On the global dimension of D + M. Canad. Math. Bull. 18 (1975), 657660.Google Scholar
[3]Greenberg, B.. Global dimension of cartesian squares. J. Algebra 32 (1974), 3143.CrossRefGoogle Scholar
[4]Greenberg, B.. Coherence in cartesian squares. J. Algebra 50 (1978), 1225.Google Scholar
[5]Milnor, J.. Introduction to Algebraic K-theory. Annals Math. Studies, vol. 72 (University Press, Princeton, 1971).Google Scholar
[6]Vasconcelos, W. V.. Rings of Dimension Two. Lecture Notes in Pure and Applied Mathematics, vol. 22 (Marcel Dekker, 1976).Google Scholar