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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Strong incompactness for some nonperfect rings
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by Jan Trlifaj PDF
Proc. Amer. Math. Soc. 123 (1995), 21-25 Request permission

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
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 21-25
  • MSC: Primary 16D40; Secondary 03E75, 16E50
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1212288-6
  • MathSciNet review: 1212288