JournalsrsmupVol. 135pp. 133–149

Strongly FP-injective and strongly flat functors

  • Lixin Mao

    Nanjing Institute of Technology, Nanjing, Jiangsu, China
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Abstract

A functor FF \in (mod-RR, Ab) is called strongly FP-injective if FF is isomorphic to some functor M- \otimes M in (mod-RR, Ab) with MM an FP-injective left RR-module. A functor GG \in ((mod-R)opR)^{\mathrm {op}} Ab) is said to be strongly flat if GG is isomorphic to some functor (,N)(-,N) in ((mod-R)opR)^{\mathrm {op}}, Ab) with NN a flat right RR-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