TY - JOUR
T1 - Ding injective envelopes in the category of complexes
AU - Gillespie, James
AU - Iacob, Alina
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature.
PY - 2023/3
Y1 - 2023/3
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 - http://www.scopus.com/inward/record.url?scp=85123641652&partnerID=8YFLogxK
U2 - 10.1007/s12215-021-00706-7
DO - 10.1007/s12215-021-00706-7
M3 - Article
AN - SCOPUS:85123641652
SN - 0009-725X
VL - 72
SP - 997
EP - 1004
JO - Rendiconti del Circolo Matematico di Palermo
JF - Rendiconti del Circolo Matematico di Palermo
IS - 2
ER -