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...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Communications in algebra Ročník 52; číslo 5; s. 1818 - 1825
Hlavní autoři: Taşdemir, Özgür, Koşan, M. Tamer
Médium: Journal Article
Jazyk:angličtina
Vydáno: Abingdon Taylor & Francis 03.05.2024
Taylor & Francis Ltd
Témata:
(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
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2023.2274951