Kernel-endoregular modules and the morphic property - Taşdemir, Özgür; Koşan, M. Tamer (Communications in algebra, 2024)
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.