# Strongly FP-injective and strongly flat functors

### Lixin Mao

Nanjing Institute of Technology, Nanjing, Jiangsu, China

## Abstract

A functor $F \in$ (mod-$R$, Ab) is called *strongly FP-injective* if $F$ is isomorphic to some functor $- \otimes M$ in (mod-$R$, Ab) with $M$ an FP-injective left $R$-module. A functor $G \in$ ((mod-$R)^{\mathrm {op}}$ Ab) is said to be *strongly flat* if $G$ is isomorphic to some functor $(-,N)$ in ((mod-$R)^{\mathrm {op}}$, Ab) with $N$ a flat right $R$-module. We study the properties of strongly FP-injective functors and explore the relationship between strongly FP-injective functors and strongly flat functors. Precovers and preenvelopes by strongly FP-injective and strongly flat functors are also investigated.

## Cite this article

Lixin Mao, Strongly FP-injective and strongly flat functors. Rend. Sem. Mat. Univ. Padova 135 (2016), pp. 133–149

DOI 10.4171/RSMUP/135-7