Gorenstein Projective Precovers

Sergio Estrada; Alina Iacob; Katelyn A. Coggins; Katelyn Yeomans

doi:10.1007/s00009-016-0822-5

Gorenstein Projective Precovers

Sergio Estrada, Alina Iacob, Katelyn A. Coggins, Katelyn Yeomans

Mathematical Sciences

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

11 Scopus citations

Abstract

We prove that the class of Gorenstein projective modules is special precovering over any left GF-closed ring such that every Gorenstein projective module is Gorenstein flat and every Gorenstein flat module has finite Gorenstein projective dimension. This class of rings includes (strictly) Gorenstein rings, commutative noetherian rings of finite Krull dimension, as well as right coherent and left n-perfect rings. In Sect. 4 we give examples of left GF-closed rings that have the desired properties (every Gorenstein projective module is Gorenstein flat and every Gorenstein flat has finite Gorenstein projective dimension) and that are not right coherent.

Original language	English
Article number	33
Journal	Mediterranean Journal of Mathematics
Volume	14
Issue number	1
DOIs	https://doi.org/10.1007/s00009-016-0822-5
State	Published - Feb 1 2017

Keywords

Gorenstein flat
Gorenstein projective
precover

Access to Document

10.1007/s00009-016-0822-5

Cite this

@article{417484d73b2d49a4a79a9b34de571fce,

title = "Gorenstein Projective Precovers",

abstract = "We prove that the class of Gorenstein projective modules is special precovering over any left GF-closed ring such that every Gorenstein projective module is Gorenstein flat and every Gorenstein flat module has finite Gorenstein projective dimension. This class of rings includes (strictly) Gorenstein rings, commutative noetherian rings of finite Krull dimension, as well as right coherent and left n-perfect rings. In Sect. 4 we give examples of left GF-closed rings that have the desired properties (every Gorenstein projective module is Gorenstein flat and every Gorenstein flat has finite Gorenstein projective dimension) and that are not right coherent.",

keywords = "Gorenstein flat, Gorenstein projective, precover",

author = "Sergio Estrada and Alina Iacob and Coggins, {Katelyn A.} and Katelyn Yeomans",

note = "Publisher Copyright: {\textcopyright} 2017, Springer International Publishing.",

year = "2017",

month = feb,

day = "1",

doi = "10.1007/s00009-016-0822-5",

language = "English",

volume = "14",

journal = "Mediterranean Journal of Mathematics",

issn = "1660-5446",

publisher = "Birkhauser Verlag Basel",

number = "1",

}

TY - JOUR

T1 - Gorenstein Projective Precovers

AU - Estrada, Sergio

AU - Iacob, Alina

AU - Coggins, Katelyn A.

AU - Yeomans, Katelyn

PY - 2017/2/1

Y1 - 2017/2/1

N2 - We prove that the class of Gorenstein projective modules is special precovering over any left GF-closed ring such that every Gorenstein projective module is Gorenstein flat and every Gorenstein flat module has finite Gorenstein projective dimension. This class of rings includes (strictly) Gorenstein rings, commutative noetherian rings of finite Krull dimension, as well as right coherent and left n-perfect rings. In Sect. 4 we give examples of left GF-closed rings that have the desired properties (every Gorenstein projective module is Gorenstein flat and every Gorenstein flat has finite Gorenstein projective dimension) and that are not right coherent.

AB - We prove that the class of Gorenstein projective modules is special precovering over any left GF-closed ring such that every Gorenstein projective module is Gorenstein flat and every Gorenstein flat module has finite Gorenstein projective dimension. This class of rings includes (strictly) Gorenstein rings, commutative noetherian rings of finite Krull dimension, as well as right coherent and left n-perfect rings. In Sect. 4 we give examples of left GF-closed rings that have the desired properties (every Gorenstein projective module is Gorenstein flat and every Gorenstein flat has finite Gorenstein projective dimension) and that are not right coherent.

KW - Gorenstein flat

KW - Gorenstein projective

KW - precover

UR - http://www.scopus.com/inward/record.url?scp=85009973137&partnerID=8YFLogxK

U2 - 10.1007/s00009-016-0822-5

DO - 10.1007/s00009-016-0822-5

M3 - Article

SN - 1660-5446

VL - 14

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 1

M1 - 33

ER -

Gorenstein Projective Precovers

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this