Gorenstein Injective Covers and Envelopes over Noetherian Rings

Alina Iacob; Edgar E. Enochs

doi:10.1090/S0002-9939-2014-12232-5

Gorenstein Injective Covers and Envelopes over Noetherian Rings

Alina Iacob, Edgar E. Enochs

Mathematical Sciences

University of Kentucky

Research output: Contribution to conference › Presentation

Abstract

We prove that if R is a commutative Noetherian ring such that the character modules of Gorenstein injective modules are Gorenstein flat, then the class of Gorenstein injective modules is closed under direct limits and it is covering.

We also prove that over such a ring the class of Gorenstein injective modules is enveloping. In particular this shows the existence of the Gorenstein injective envelopes over commutative Noetherian rings with dualizing complexes.

Original language	American English
DOIs	https://doi.org/10.1090/S0002-9939-2014-12232-5
State	Published - Aug 18 2014
Event	Proceedings of the American Mathematical Society (AMS) - Duration: Aug 18 2014 → …

Conference

Conference	Proceedings of the American Mathematical Society (AMS)
Period	08/18/14 → …

Keywords

Gorenstein injective covers
Nonetherian rings

DC Disciplines

Education
Mathematics

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https://doi.org/10.1090/S0002-9939-2014-12232-5

Cite this

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title = "Gorenstein Injective Covers and Envelopes over Noetherian Rings",

abstract = " We prove that if R is a commutative Noetherian ring such that the character modules of Gorenstein injective modules are Gorenstein flat, then the class of Gorenstein injective modules is closed under direct limits and it is covering. We also prove that over such a ring the class of Gorenstein injective modules is enveloping. In particular this shows the existence of the Gorenstein injective envelopes over commutative Noetherian rings with dualizing complexes.",

keywords = "Gorenstein injective covers, Nonetherian rings",

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

year = "2014",

month = aug,

day = "18",

doi = "10.1090/S0002-9939-2014-12232-5",

language = "American English",

note = "Proceedings of the American Mathematical Society (AMS) ; Conference date: 18-08-2014",

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TY - CONF

T1 - Gorenstein Injective Covers and Envelopes over Noetherian Rings

AU - Iacob, Alina

AU - Enochs, Edgar E.

PY - 2014/8/18

Y1 - 2014/8/18

N2 - We prove that if R is a commutative Noetherian ring such that the character modules of Gorenstein injective modules are Gorenstein flat, then the class of Gorenstein injective modules is closed under direct limits and it is covering. We also prove that over such a ring the class of Gorenstein injective modules is enveloping. In particular this shows the existence of the Gorenstein injective envelopes over commutative Noetherian rings with dualizing complexes.

AB - We prove that if R is a commutative Noetherian ring such that the character modules of Gorenstein injective modules are Gorenstein flat, then the class of Gorenstein injective modules is closed under direct limits and it is covering. We also prove that over such a ring the class of Gorenstein injective modules is enveloping. In particular this shows the existence of the Gorenstein injective envelopes over commutative Noetherian rings with dualizing complexes.

KW - Gorenstein injective covers

KW - Nonetherian rings

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/81

UR - https://doi.org/10.1090/S0002-9939-2014-12232-5

U2 - 10.1090/S0002-9939-2014-12232-5

DO - 10.1090/S0002-9939-2014-12232-5

M3 - Presentation

T2 - Proceedings of the American Mathematical Society (AMS)

Y2 - 18 August 2014

ER -

Gorenstein Injective Covers and Envelopes over Noetherian Rings

Abstract

Conference

Keywords

DC Disciplines

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