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 …

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 …

Tilting and Cotilting in Functor Categories

J Wang, T Zhao - Mathematics, 2022 - mdpi.com
Mathematics | Free Full-Text | Tilting and Cotilting in Functor Categories | HTML Next Article in
Journal Preliminary Results on the Preinduction Cervix Status by Shear Wave Elastography …

Baer–Kaplansky Classes in Grothendieck Categories and Applications

S Crivei, D Keskin Tütüncü - Mediterranean Journal of Mathematics, 2019 - Springer
Abstract We study Baer–Kaplansky classes in Grothendieck categories. We apply our results
to functor categories, and discuss the transfer of the Baer–Kaplansky property to finitely …

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 …

Higher phantom morphisms with respect to a subfunctor of Ext

L Mao - Algebras and Representation Theory, 2019 - Springer
A morphism f: M→ N f:M→N of left R-modules is called an n-phantom morphism (resp. a Tor
n-epimorphism) if the induced morphism Tor n (A, f)= 0 (resp. Tor n (A, f) is an epimorphism) …

Some precovers and preenvelopes in functor categories

Z Xie, Z Liu - Indian Journal of Pure and Applied Mathematics, 2021 - Springer
Let n≥ 1 be an integer. A functor F∈(mod-R, Ab) is called n-strongly FP-injective if F is
isomorphic to some functor-⊗ M in (mod-R, Ab) with M an FP n-injective left R-module. A …

On n-phantom and n-Ext-phantom Morphisms

K Lan, B Lu - Taiwanese Journal of Mathematics, 2021 - JSTOR
This paper extends many conclusions based on phantom envelopes and Ext-phantom
covers of modules, and we find that many important properties still hold after replacing …

Strongly FP-injective and strongly flat functors

L Mao - Rendiconti del Seminario Matematico della Università …, 2016 - ems.press
Given a ring R, denote by mod-R the category of nitely presented right R-modules, the two
functor categories (mod-R, Ab) and ((mod-R) op, Ab) with values in the category Ab of …

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 …