#### Title

Gorenstein Flat Preenvelopes

#### Document Type

Presentation

#### Publication Date

9-1-2015

#### Abstract

We consider a two sided noetherian ring R such that the character modules of Gorenstein injective left R-modules are Gorenstein ﬂat right R-modules. We then prove that the class of Gorenstein ﬂat right R-modules is preenveloping. We also show that over such a ring the class of Gorenstein ﬂat complexes of right R-modules is preenevloping in Ch(R). We also give examples of rings with the property that the character modules of Gorenstein injective modules are Gorenstein ﬂat. We show that any two sided noetherian ring R of ﬁnite self injective dimension as a right R-module has the desired property. And we prove that if R is a two sided noetherian ring with a dualizing bimodule V, and such that R is left n-perfect for some positive integer n, then the character modules of Gorenstein injective modules are Gorenstein ﬂat.

#### Sponsorship/Conference/Institution

Some Trends in Algebra Annual Conference (STA)

#### Location

Prague, Czech Republic

#### Recommended Citation

Iacob, Alina.
2015.
"Gorenstein Flat Preenvelopes."
*Mathematical Sciences Faculty Presentations*.
Presentation 237.

https://digitalcommons.georgiasouthern.edu/math-sci-facpres/237