Direct sums of completely almost self-injective modules. (English) Zbl 1398.16006
López-Permouth, Sergio R. (ed.) et al., Advances in rings and modules. Dedicated to Bruno J. Müller. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-3555-4/pbk; 978-1-4704-4901-8/ebook). Contemporary Mathematics 715, 273-283 (2018).
Summary: For any two modules \(M\) and \(N\) over a ring \(R\), the concept of \(M\) being almost \(N\)-injective was introduced by Y. Baba in [Osaka J. Math. 26, No. 3, 687–698 (1989; Zbl 0701.16004)]. A module \(M\) is said to be completely almost self-injective, if for any two subfactors \(A\), \(B\) of \(M\), \(A\) is amost \(B\)-injective. The structure theory of completely almost self-injective modules has been developed by the author [J. Algebra 478, 353–366 (2017; Zbl 1405.16002)] and he has given a characterization of these modules. A direct sum of two completely almost self-injective modules need not be completely almost self-injective. In this paper, direct sums of completely almost self-injective modules are studied. Among other results, it has been proved that if a ring \(R\) is completely almost self-injective, then any finitely generated \(R\)-modules is completely almost self-injective.
For the entire collection see [Zbl 1401.16001].
For the entire collection see [Zbl 1401.16001].
MSC:
| 16D50 | Injective modules, self-injective associative rings |
| 16E50 | von Neumann regular rings and generalizations (associative algebraic aspects) |
Keywords:
\(M\)-injectives; \(M\)-projectives; uniform modules; uniserial modules; von Neumann regular ringsReferences:
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