Dergiler / Turkish Journal of Mathematics / 2013 / Cilt: 37 - Sayı: 2
Strongly Gorenstein flat and Gorenstein FP-injective modules
- Sayfa
- 218–230
- DOI
- —
Özet
In this paper, we first study the properties of strongly Gorenstein flat (resp. Gorenstein FP-injective) modules which are special Gorenstein projective (resp. Gorenstein injective) modules, and use them to prove that the global strongly Gorenstein flat dimension and the global Gorenstein FP-injective dimension of a ring R are identical when R is n-FC or commutative coherent. Finally, we show that if R is a commutative Noetherian ring, then, for any R-module M, SGfdRM=GpdRM, and hence SGfdRM< \infty if and only if GfdRM
Abstract
In this paper, we first study the properties of strongly Gorenstein flat (resp. Gorenstein FP-injective) modules which are special Gorenstein projective (resp. Gorenstein injective) modules, and use them to prove that the global strongly Gorenstein flat dimension and the global Gorenstein FP-injective dimension of a ring R are identical when R is n-FC or commutative coherent. Finally, we show that if R is a commutative Noetherian ring, then, for any R-module M, SGfdRM=GpdRM, and hence SGfdRM< \infty if and only if GfdRM