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Ding injective envelopes in the category of complexes
- Source :
- Rendiconti del Circolo Matematico di Palermo Series 2. 72:997-1004
- Publication Year :
- 2022
- Publisher :
- Springer Science and Business Media LLC, 2022.
-
Abstract
- A complex $X$ is called Ding injective if there exists an exact sequence of injective complexes $\ldots \rightarrow E_1 \rightarrow E_0 \rightarrow E_{-1} \rightarrow \ldots$ such that $X = Ker(E_0 \rightarrow E_{-1})$, and the sequence remains exact when the functor $Hom(A,-)$ is applied to it, for any $FP$-injective complex $A$. We prove that, over any ring $R$, a complex is Ding injective if and only if it is a complex of Ding injective modules. We use this to show that the class of Ding injective complexes is enveloping over any ring.
Details
- ISSN :
- 19734409 and 0009725X
- Volume :
- 72
- Database :
- OpenAIRE
- Journal :
- Rendiconti del Circolo Matematico di Palermo Series 2
- Accession number :
- edsair.doi.dedup.....ce5fe87f05fd256de149a08cc1e46196