On modules and rings having large absolute direct summands

An ADS module is a direct sum of mutually injective modules, and an e-ADS module is a direct sum of mutually automorphism-invariant modules. In this paper, we introduce and study large ADS (LADS) modules that form a class of modules larger than ADS modules. An LADS module is a direct sum of mutually...

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Bibliographic Details
Published in:Communications in algebra 2023-12, Vol.51 (12), p.4949-4961
Main Authors: Dao Thi, Trang, M. Koşan, Tamer, Taşdemir, Özgür, Truong Cong, Quynh
Format: Article
Language:English
Subjects:
(large) ADS module
(large) ADS ring
Automorphism-invariant module
Automorphisms
CS module
essentially injective
fully invariant submodule
Modules
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Summary:An ADS module is a direct sum of mutually injective modules, and an e-ADS module is a direct sum of mutually automorphism-invariant modules. In this paper, we introduce and study large ADS (LADS) modules that form a class of modules larger than ADS modules. An LADS module is a direct sum of mutually essentially injective modules. This result corresponds to the results of ADS and e-ADS modules. Communicated by Toma Albu
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2023.2223301