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

Abstract

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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Correspondence to Pace P. Nielsen.

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Nielsen, P.P. The behavior of ascending chain conditions on submodules of bounded finite generation in direct sums. Isr. J. Math. 215, 339–347 (2016). https://doi.org/10.1007/s11856-016-1381-y

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