Israel Journal of Mathematics

, Volume 215, Issue 1, pp 339–347 | Cite as

The behavior of ascending chain conditions on submodules of bounded finite generation in direct sums

  • Pace P. Nielsen


We construct a ring R which has the ascending chain condition on n-generated right ideals for each n ≥ 1 (also called the right pan-acc property), such that no full matrix ring over R has the ascending chain condition on cyclic right ideals. Thus, the right pan-acc property is not a Morita invariant. Moreover, a direct sum of (free) modules with pan-acc does not necessarily even have 1-acc.


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© Hebrew University of Jerusalem 2016

Authors and Affiliations

  1. 1.Department of MathematicsBrigham Young UniversityProvoUSA

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