Gorenstein Flat Preenvelopes
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.
Some Trends in Algebra Annual Conference (STA)
Prague, Czech Republic
"Gorenstein Flat Preenvelopes."
Mathematical Sciences Faculty Presentations.