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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Strong incompactness for some nonperfect rings


Author: Jan Trlifaj
Journal: Proc. Amer. Math. Soc. 123 (1995), 21-25
MSC: Primary 16D40; Secondary 03E75, 16E50
MathSciNet review: 1212288
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Abstract: Answering a question of Eklof and Mekler, for each regular uncountable cardinal $ \kappa $, we construct a non-left-perfect ring $ {R_\kappa }$ and a non-projective strongly $ \kappa $-free left ideal $ {I_\kappa }$ such that $ {\text{gen}}({I_\kappa }) = \kappa $. Moreover, if $ \kappa > {\aleph _1}$, then $ {I_\kappa }$ is not $ \kappa $-free. As consequences, we obtain results concerning incompactness spectra of non-perfect rings.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1212288-6
PII: S 0002-9939(1995)1212288-6
Keywords: Almost free module, non-left-perfect ring, $ \kappa $-free, strongly $ \kappa $-free, incompactness spectrum
Article copyright: © Copyright 1995 American Mathematical Society