Ding injective envelopes in the category of complexes

James Gillespie; Alina Iacob

doi:10.1007/s12215-021-00706-7

Ding injective envelopes in the category of complexes

James Gillespie
, Alina Iacob

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

A complex X is called Ding injective if there exists an exact sequence of injective complexes … → E₁→ E→ E_{- 1}→ … such that X= Ker(E→ 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.

Original language	English
Pages (from-to)	997-1004
Number of pages	8
Journal	Rendiconti del Circolo Matematico di Palermo
Volume	72
Issue number	2
DOIs	https://doi.org/10.1007/s12215-021-00706-7
State	Published - Jan 27 2022

Scopus Subject Areas

General Mathematics

Keywords

Ding injective complexes
Ding injective envelope
Ding injective modules

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10.1007/s12215-021-00706-7

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title = "Ding injective envelopes in the category of complexes",

abstract = "A complex X is called Ding injective if there exists an exact sequence of injective complexes … → E1→ E→ E- 1→ … such that X= Ker(E→ 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.",

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T1 - Ding injective envelopes in the category of complexes

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AU - Iacob, Alina

PY - 2022/1/27

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N2 - A complex X is called Ding injective if there exists an exact sequence of injective complexes … → E1→ E→ E- 1→ … such that X= Ker(E→ 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.

AB - A complex X is called Ding injective if there exists an exact sequence of injective complexes … → E1→ E→ E- 1→ … such that X= Ker(E→ 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.

KW - Ding injective complexes

KW - Ding injective envelope

KW - Ding injective modules

UR - https://www.scopus.com/pages/publications/85123641652

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M3 - Article

AN - SCOPUS:85123641652

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VL - 72

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JO - Rendiconti del Circolo Matematico di Palermo

JF - Rendiconti del Circolo Matematico di Palermo

IS - 2

ER -

Ding injective envelopes in the category of complexes

Abstract

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Keywords

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