Small Dual-ADS Modules, Small ADS and Small ADS Modules
A right module over a ring is called small dual-ADS, if for each decomposition then and are mutually small projective. Small dual-ADS modules are the dual analogue of LADS modules, a class of modules recently studied. In this article, we study several properties of these modules. It is shown that a...
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| Veröffentlicht in: | Lobachevskii journal of mathematics 2023-12, Vol.44 (12), p.5097-5115 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
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| Online-Zugang: | Volltext |
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| Zusammenfassung: | A right module
over a ring
is called small dual-ADS, if for each decomposition
then
and
are mutually small projective. Small dual-ADS modules are the dual analogue of LADS modules, a class of modules recently studied. In this article, we study several properties of these modules. It is shown that a module
is small dual-ADS if and only if for every decomposition
and
a submodule of
with
and
a co-essential submodule of
in
, then
contains a direct complement of
in
. A generalization of small dual-ADS modules are considered, namely, small ADS
-modules. We show that a module
is small ADS
if and only if for every decomposition
and any submodule
of
with
and
weak supplements of
in
, then
contains a direct complement of
in
. |
|---|---|
| ISSN: | 1995-0802 1818-9962 |
| DOI: | 10.1134/S1995080223120028 |