Co-coatomic lifting modules

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Güroğlu A. T.

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, vol.1, pp.1-9, 2025 (ESCI, Scopus)

• Publication Type: Article / Article
• Volume: 1
• Publication Date: 2025
• Doi Number: 10.1142/s1793557125501190
• Journal Name: ASIAN-EUROPEAN JOURNAL OF MATHEMATICS
• Journal Indexes: Scopus, Emerging Sources Citation Index (ESCI), zbMATH
• Page Numbers: pp.1-9
• Manisa Celal Bayar University Affiliated: Yes

Abstract

The objective of this paper is to examine the lifting modules with the assumption that a submodule can be considered as a co-coatomic. A module [Formula: see text] is called a co-coatomic lifting module if, for every proper co-coatomic submodule [Formula: see text] of [Formula: see text], there exists a decomposition [Formula: see text] of [Formula: see text] such that [Formula: see text] and [Formula: see text]. Co-coatomic lifting modules are situated between lifting modules and cofinitely lifting modules. We demonstrate that if [Formula: see text] is a distributive co-coatomic lifting module, then [Formula: see text] is also co-coatomic lifting for any submodule [Formula: see text] of [Formula: see text]. Moreover, the co-coatomic direct summand of a co-coatomic lifting module is co-coatomic lifting. If every [Formula: see text]-module [Formula: see text] is co-coatomic lifting, then [Formula: see text] is semiperfect. Furthermore, we derive that a finitely generated co-coatomic lifting module is discrete under certain condition.