Kernel-endoregular modules and the morphic property

This paper describes properties of three certain classes of modules M over a ring R determined by conditions on isomorphic direct summands ( ≲ ⊕ ): The condition that whenever ( I m λ ≅ ) M / Ker λ ≲ ⊕ M then Ker λ and I m λ are direct summands of M for any endomorphism λ ∈ End ( M ) (kernel-endoreg...

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Bibliographic Details
Published in:Communications in algebra Vol. 52; no. 5; pp. 1818 - 1825
Main Authors: Taşdemir, Özgür, Koşan, M. Tamer
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 03.05.2024
Taylor & Francis Ltd
Subjects:
(co-)Hopfian module
(dual-)Rickart module
C2 modules
D2 modules
endoregular module
Modules
morphic module
Primary: 16D10
unit-regular module
ISSN:0092-7872, 1532-4125
Online Access:Get full text
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Summary:This paper describes properties of three certain classes of modules M over a ring R determined by conditions on isomorphic direct summands ( ≲ ⊕ ): The condition that whenever ( I m λ ≅ ) M / Ker λ ≲ ⊕ M then Ker λ and I m λ are direct summands of M for any endomorphism λ ∈ End ( M ) (kernel-endoregular modules). The condition that if M / A ≅ B where A, B ≲ ⊕ M then M / B ≅ A (iso-summand-morphic modules). The condition if M / A ≅ B where A, B ≤ ⊕ M , then M / B ≅ A (summand-morphic modules) which is precisely the internal cancellation property for modules.
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content type line 14
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2023.2274951