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

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 invarian...

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Bibliographic Details
Published in:Israel journal of mathematics 2016-09, Vol.215 (1), p.339-347
Main Author: Nielsen, Pace P.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Chains
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Modules
Theoretical
Citations: Items that this one cites
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Summary: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.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-016-1381-y