Abstract
The main aim of this paper is to determine how far a module is from tilting or cotilting. With this in mind, we introduce T n m -injective modules and T n m -projective modules for any non-negative integers m, n and any Wakamatsu tilting module T, and then give some of their characterizations. In particular, for a tilting module T which satisfies an F.S. condition such that Add T is closed under submodules, we show that if \( \frac{M} {N} \) belongs to Prod T, then submodules of T are T 0 m -projective.
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References
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Nikmehr, M.J., Shaveisi, F. (2010). A Generalization of Homological Dimensions. In: Albu, T., Birkenmeier, G.F., Erdoğgan, A., Tercan, A. (eds) Ring and Module Theory. Trends in Mathematics. Springer, Basel. https://doi.org/10.1007/978-3-0346-0007-1_10
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DOI: https://doi.org/10.1007/978-3-0346-0007-1_10
Publisher Name: Springer, Basel
Print ISBN: 978-3-0346-0006-4
Online ISBN: 978-3-0346-0007-1
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