The ℵ1-Product of DG-Injective Complexes

Edgar E. Enochs; Alina Iacob

doi:10.1017/S0013091505000143

The ℵ1-Product of DG-Injective Complexes

Edgar E. Enochs, Alina Iacob

Mathematical Sciences

University of Kentucky

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

8 Scopus citations

Abstract

<div class="line" id="line-19"> Given a left Noetherian ring R, we give a necessary and su&ffilig;cient condition in order that a complex of R-modules be DG-injective. Using this result we prove that if (Ki)i∈I is family of DG-injective complexes of left R-modules and K is the 1-product of (Ki)i∈I (i.e. K&alefsym; ⊂ i I Ki is such that, for each n, Kn ⊂ i∈I Kn/i consists of all (xi)i∈I such that {i | xi xi=/=0} is at most countable), then K is DG-injective.</div><div class="line" id="line-34"> <br/></div>

Original language	American English
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	49
DOIs	https://doi.org/10.1017/S0013091505000143
State	Published - Jun 2006

Keywords

DG-injective complexes
Exact precover
ℵ-products

DC Disciplines

Physical Sciences and Mathematics

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title = "The ℵ1-Product of DG-Injective Complexes",

abstract = " Given a left Noetherian ring R, we give a necessary and su&ffilig;cient condition in order that a complex of R-modules be DG-injective. Using this result we prove that if (Ki)i∈I is family of DG-injective complexes of left R-modules and K is the 1-product of (Ki)i∈I (i.e. K&alefsym; ⊂ i I Ki is such that, for each n, Kn ⊂ i∈I Kn/i consists of all (xi)i∈I such that {i | xi xi=/=0} is at most countable), then K is DG-injective. ",

keywords = "DG-injective complexes, Exact precover, ℵ-products",

author = "Enochs, {Edgar E.} and Alina Iacob",

note = "THE $\aleph_1$-PRODUCT OF DG-INJECTIVE COMPLEXES - Volume 49 Issue 2 - Edgar E. Enochs, Alina Iacob",

year = "2006",

month = jun,

doi = "10.1017/S0013091505000143",

language = "American English",

volume = "49",

journal = "Proceedings of the Edinburgh Mathematical Society",

issn = "0013-0915",

publisher = "Cambridge University Press",

}

TY - JOUR

T1 - The ℵ1-Product of DG-Injective Complexes

AU - Enochs, Edgar E.

AU - Iacob, Alina

N1 - THE $\aleph_1$-PRODUCT OF DG-INJECTIVE COMPLEXES - Volume 49 Issue 2 - Edgar E. Enochs, Alina Iacob

PY - 2006/6

Y1 - 2006/6

N2 - Given a left Noetherian ring R, we give a necessary and su&ffilig;cient condition in order that a complex of R-modules be DG-injective. Using this result we prove that if (Ki)i∈I is family of DG-injective complexes of left R-modules and K is the 1-product of (Ki)i∈I (i.e. K&alefsym; ⊂ i I Ki is such that, for each n, Kn ⊂ i∈I Kn/i consists of all (xi)i∈I such that {i | xi xi=/=0} is at most countable), then K is DG-injective.

AB - Given a left Noetherian ring R, we give a necessary and su&ffilig;cient condition in order that a complex of R-modules be DG-injective. Using this result we prove that if (Ki)i∈I is family of DG-injective complexes of left R-modules and K is the 1-product of (Ki)i∈I (i.e. K&alefsym; ⊂ i I Ki is such that, for each n, Kn ⊂ i∈I Kn/i consists of all (xi)i∈I such that {i | xi xi=/=0} is at most countable), then K is DG-injective.

KW - DG-injective complexes

KW - Exact precover

KW - ℵ-products

UR - https://doi.org/10.1017/S0013091505000143

U2 - 10.1017/S0013091505000143

DO - 10.1017/S0013091505000143

M3 - Article

SN - 0013-0915

VL - 49

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

ER -

The ℵ1-Product of DG-Injective Complexes

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Keywords

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