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- W2057917952 abstract "Using Lambek torsion as the torsion theory, we investigate the question of when an Abelian group G is torsion as a module over its endomorphism ring E . Groups that are torsion modules in this sense are called ℒ-torsion. Among the classes of torsion and truly mixed Abelian groups, we are able to determine completely those groups that are ℒ-torsion. However, the case when G is torsion free is more complicated. Whereas no torsion-free group of finite rank is ℒ-torsion, we show that there are large classes of torsion-free groups of infinite rank that are ℒ-torsion. Nevertheless, meaningful definitive criteria for a torsion-free group to be ℒ-torsion have not been found." @default.
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- W2057917952 date "2001-10-01" @default.
- W2057917952 modified "2023-09-27" @default.
- W2057917952 title "Abelian groups that are torsion over their endomorphism rings" @default.
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- W2057917952 doi "https://doi.org/10.1017/s0004972700039915" @default.
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