On generalizations of strongly $ ss $-discrete modules

Yıldız Aydın; Burcu Nişancı Türkmen; Yıldız Aydın; Burcu Nişancı Türkmen

doi:10.3934/math.2026362

AIMS Mathematics

2026, Volume 11, Issue 3: 8812-8831. doi: 10.3934/math.2026362

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Research article

On generalizations of strongly $ ss $-discrete modules

Yıldız Aydın ^{1
,
,},
Burcu Nişancı Türkmen ²

1.
Department of Management Information Systems, Faculty of Economics, Administrative and Social Sciences, İstanbul Gelişim University, Avcılar, 34310, İstanbul, Türkiye
2.
Department of Mathematics, Faculty of Science and Arts, Amasya University, İpekköy, 05100, Amasya, Türkiye

Received: 28 October 2025 Revised: 17 March 2026 Accepted: 27 March 2026 Published: 31 March 2026
MSC : 16D10, 16D40, 16D70

In this paper, we introduced the notions of $ \mathcal{LA} $-lifting modules and $ \mathcal{LA} $-discrete modules, which are strong concepts of lifting modules and discrete modules, respectively. We provided some conditions of these modules and generalizations of $ ss $-lifting modules and $ ss $-discrete modules, respectively. Finally, we characterized $ \mathcal{LA} $-lifting modules via left perfect rings and strongly $ \mathcal{LA} $-discrete rings by using the notion of semiperfect rings.
- locally Artinian modules,
- locally Artinian supplemented modules,
- lifting modules,
- $ \mathcal{LA} $-lifting modules,
- discrete modules,
- $ \mathcal{LA} $-discrete modules,
- perfect rings,
- semiperfect rings
Citation: Yıldız Aydın, Burcu Nişancı Türkmen. On generalizations of strongly $ ss $-discrete modules[J]. AIMS Mathematics, 2026, 11(3): 8812-8831. doi: 10.3934/math.2026362

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Abstract

In this paper, we introduced the notions of $ \mathcal{LA} $-lifting modules and $ \mathcal{LA} $-discrete modules, which are strong concepts of lifting modules and discrete modules, respectively. We provided some conditions of these modules and generalizations of $ ss $-lifting modules and $ ss $-discrete modules, respectively. Finally, we characterized $ \mathcal{LA} $-lifting modules via left perfect rings and strongly $ \mathcal{LA} $-discrete rings by using the notion of semiperfect rings.

References

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