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Ranks of modules relative to a torsion theory
Relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $M$, called {em $tau$-rank of} $M$, which coincides with the reduced rank of $M$ whenever $tau$ is the Goldie torsion theory. It is shown that the $tau$-rank of $M$ is measured by the length of certain decompositions of the $tau$-injective hull of $M$. Moreover, some relations between the $tau$-rank of $M$ and c...
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ژورنال
عنوان ژورنال: Measurement
سال: 2018
ISSN: 0263-2241
DOI: 10.1016/j.measurement.2017.10.053