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A note on Morita context functors
Published online by Cambridge University Press: 24 October 2008
Extract
It is claimed in [3], proposition 4 that if a Morita context (R, V, W, S) is such that WVW = W and S/WV is flat as a right S-module, then Vω = 0, ω ∈ W, implies ω = 0. The proof given for this uses proposition 5 of Azumaya[l] in which rings have unity and so is only applicable when the ring S has a unity. Thus proposition 4 in [3] should be amended so that the additional hypothesis that S has a unity is imposed for statement (4) to be equivalent to the first three statements. It is the purpose of this note to give an example to show that the claim in [3] is false in general.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 107 , Issue 2 , March 1990 , pp. 273 - 274
- Copyright
- Copyright © Cambridge Philosophical Society 1990
References
REFERENCES
[1]Azumaya, G.. Some properties of TTT-classes. In Proceedings of Conference on Orders, Group Rings and Related Topics, Lecture Notes in Math. vol. 353 (Springer-Verlag, 1973), pp. 72–83.CrossRefGoogle Scholar
[2]Cohen, M. and Montgomery, S.. Group-graded rings, smash products, and group actions. Trans. Amer. Math. Soc. 282 (1984), 237–258.CrossRefGoogle Scholar
[3]Nicholson, W. K. and Watters, J. F.. Morita context functors. Math. Proc. Cambridge Philos. Soc. 103 (1988), 399–408.CrossRefGoogle Scholar