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articleNo Access
ON TEST MODULES FOR FLAT DIMENSION
- JAVIER MAJADAS
Journal of Algebra and Its Applications31 Oct 2013
Preview Abstract
A ring with a test module of finite upper complete intersection dimension is complete intersection.
articleNo Access
Some homological properties of generalized local cohomology modules
- Yavar Irani,
- Kamal Bahmanpour, and
- Ghader Ghasemi
Journal of Algebra and Its Applications03 Nov 2019
Preview Abstract
Let $(R, 𝔪)$ be a Noetherian local ring and $M$ , $N$ be two finitely generated $R$ -modules. In this paper, it is shown that
${id}_{R_{𝔭}} H_{𝔭 R_{𝔭}}^{i} (M_{𝔭}, N_{𝔭}) \leq {id}_{R} H_{𝔪}^{i + dim R / 𝔭} (M, N)$
and
${fd}_{R_{𝔭}} H_{𝔭 R_{𝔭}}^{i} (M_{𝔭}, N_{𝔭}) \leq {fd}_{R} H_{𝔪}^{i + dim R / 𝔭} (M, N),$
for each $𝔭 \in Spec R$ and each integer $i \geq 0$ . In particular, if $H_{𝔭 R_{𝔭}}^{i} (M_{𝔭}, N_{𝔭}) \neq 0$ then $H_{𝔪}^{i + dim R / 𝔭} (M, N) \neq 0$ . Moreover, some applications of these results will be included.
articleNo Access
A Note on Gorenstein Flat Dimension
- Driss Bennis
Algebra Colloquium01 Mar 2011
Preview Abstract
Unlike the Gorenstein projective and injective dimensions, the majority of results on the Gorenstein flat dimension have been established only over Noetherian (or coherent) rings. Naturally, one would like to generalize these results to any associative ring. In this direction, we show that the Gorenstein flat dimension is a refinement of the classical flat dimension over any ring; and we investigate the relations between the Gorenstein projective dimension and the Gorenstein flat dimension.
articleNo Access
Complete Intersection Flat Dimension and the Intersection Theorem
- Parviz Sahandi,
- Tirdad Sharif, and
- Siamak Yassemi
Algebra Colloquium31 Oct 2012
Preview Abstract
Any finitely generated module M over a local ring R is endowed with a complete intersection dimension CI-dim_RM and a Gorenstein dimension G-dim_RM. The Gorenstein dimension can be extended to all modules over the ring R. This paper presents a similar extension for the complete intersection dimension, and mentions the relation between this dimension and the Gorenstein flat dimension. In addition, we show that in the intersection theorem, the flat dimension can be replaced by the complete intersection flat dimension.