\(t\)-generalized supplemented modules. (English) Zbl 1381.16004
Ukr. Math. J. 67, No. 11, 1678-1686 (2016) and Ukr. Mat. Zh. 67, No. 11, 1491-1497 (2015).
Summary: In the present paper, \(t\)-generalized \(\otimes\)-supplemented modules are defined starting from the generalized supplemented modules. In addition, we present examples separating the \(t\)-generalized supplemented modules, supplemented modules, and generalized \(\otimes\)-supplemented modules and also show the equality of these modules for projective and finitely generated modules. Moreover, we define cofinitely \(t\)-generalized supplemented modules and give the characterization of these modules. Furthermore, for any ring \(R\), we show that any finite direct sum of \(t\)-generalized supplemented \(R\)-modules is \(t\)-generalized supplemented and that any direct sum of cofinitely \(t\)-generalized supplemented \(R\)-modules is a cofinitely \(t\)-generalized supplemented module.
MSC:
| 16D70 | Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) |
| 16D80 | Other classes of modules and ideals in associative algebras |
Keywords:
\(t\)-generalized supplemented modules; \(\otimes\)-supplemented modules; finitely generated modulesReferences:
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