Neat-phantom and clean-cophantom morphisms
L Mao - Journal of Algebra and Its Applications, 2021 - World Scientific
Let ℱ 𝒫∞ R be the class of all left R-modules M which has a projective resolution by finitely
generated projectives. An exact sequence 0→ A→ B→ C→ 0 of right R-modules is called …
generated projectives. An exact sequence 0→ A→ B→ C→ 0 of right R-modules is called …
Neat-flat modules
E Büyükaşık, Y Durğun - Communications in Algebra, 2016 - Taylor & Francis
Let R be a ring. A right R-module M is said to be neat-flat if the kernel of any epimorphism
Y→ M is neat in Y, ie, the induced map Hom (S, Y)→ Hom (S, M) is surjective for any simple …
Y→ M is neat in Y, ie, the induced map Hom (S, Y)→ Hom (S, M) is surjective for any simple …
Neat-flat modules
Y Buyukasik, Y Durgun - Communications in Algebra, 2016 - avesis.cu.edu.tr
Let R be a ring. A right R-module M is said to be neat-flat if the kernel of any epimorphism Y-
> M is neat in Y, ie, the induced map Hom (S, Y)-> Hom (S, M) is surjective for any simple …
> M is neat in Y, ie, the induced map Hom (S, Y)-> Hom (S, M) is surjective for any simple …
Precovers and preenvelopes by phantom and Ext-phantom morphisms
L Mao - Communications in Algebra, 2016 - Taylor & Francis
A morphism f: M→ N of left R-modules is called a phantom morphism if the induced
morphism for every (finitely presented) right R-module A. Similarly, a morphism g: M→ N of …
morphism for every (finitely presented) right R-module A. Similarly, a morphism g: M→ N of …
Neat submodules over commutative rings
E Mermut, Z Türkoğlu - Communications in Algebra, 2020 - Taylor & Francis
Let R be a commutative ring with identity. A short exact sequence E of R-modules is said to
be neat (respectively, P-pure) if the sequence Hom R (S, E)(respectively, S⊗ RE) is exact for …
be neat (respectively, P-pure) if the sequence Hom R (S, E)(respectively, S⊗ RE) is exact for …
Projectivity relative to closed (neat) submodules
Y Durğun - Journal of Algebra and Its Applications, 2022 - World Scientific
An R-module F is called closed (neat) projective if, for every closed (neat) submodule L of
every R-module M, every homomorphism from F to M/L lifts to M. In this paper, we study …
every R-module M, every homomorphism from F to M/L lifts to M. In this paper, we study …
Proper classes generated by simple modules
Z Türkoğlu - 2013 - search.proquest.com
Let Rbe a ring with unity. A short exact sequence E of left R-modules is said to be neat-exact
if every simple left R-module is projective with respect to it. We call it P-pure-exact if for every …
if every simple left R-module is projective with respect to it. We call it P-pure-exact if for every …
Higher phantom and Ext-phantom morphisms
L Mao - Journal of Algebra and Its Applications, 2018 - World Scientific
A morphism f: M→ N of left R-modules is called an n-phantom morphism if the induced
morphism Tor n R (A, f)= 0 for every (finitely presented) right R-module A. Analogously, a …
morphism Tor n R (A, f)= 0 for every (finitely presented) right R-module A. Analogously, a …
Phantom Envelopes and -Phantom Covers of Modules
L Mao - Bulletin of the Iranian Mathematical Society, 2020 - Springer
We first prove that if a monomorphism is a phantom envelope of a left R-module, then its
cokernel is pure-projective; if R is a left coherent ring and an epimorphism is an Ext Ext …
cokernel is pure-projective; if R is a left coherent ring and an epimorphism is an Ext Ext …
RD-phantom and RD-Ext-phantom Morphisms
L Mao - Filomat, 2018 - doiserbia.nb.rs
A morphism f of left R-modules is called an RD-phantom morphism if the induced morphism
Tor1 (R= aR, f)= 0 for any a R. Similarly, a morphism g of left R-modules is said to be an …
Tor1 (R= aR, f)= 0 for any a R. Similarly, a morphism g of left R-modules is said to be an …