- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:49
Rendiconti del Seminario Matematico della Università di Padova
Rend. Sem. Mat. Univ. Padova
RSMUP
0041-8994
2240-2926
General
10.4171/RSMUP
http://www.ems-ph.org/doi/10.4171/RSMUP
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2013)
135
2016
0
Strongly FP-injective and strongly flat functors
Lixin
Mao
Nanjing Institute of Technology, NANJING, JIANGSU, CHINA
Strongly FP-injective functor, FP-injective functor, strongly flat functor, flat functor, (pre)cover, (pre)envelope
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.
Associative rings and algebras
Category theory; homological algebra
133
149
10.4171/RSMUP/135-7
http://www.ems-ph.org/doi/10.4171/RSMUP/135-7