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## A FEW COMMENTS ON MATLIS DUALITY

#### Waqas Mahmood [1]

##### 205 280

For a Noetherian local ring (R, m) with p ∈ Spec(R), we denote the R-injective hull of R/p by ER(R/p). We show that it has an Rˆp -module structure, and there is an isomorphism ER(R/p) ∼= ERˆp (Rˆp/pRˆp ), where Rˆp stands for the p-adic completion of R. Moreover, for a complete Cohen-Macaulay ring R, the module D(ER(R/p)) is isomorphic to Rˆp provided that dim(R/p) = 1, where D(·) denotes the Matlis dual functor HomR(·, ER(R/m)). Here, Rˆp denotes the completion of Rp with respect to the maximal ideal pRp. These results extend those of Matlis (see [11]) shown in the case of the maximal ideal m.
Matlis duality, injective hull, local cohomology, flat covers
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Other ID JA67UZ27CM Articles Author: Waqas Mahmood
 Bibtex @ { ieja266238, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Abdullah HARMANCI}, year = {2014}, pages = {66 - 76}, doi = {10.24330/ieja.266238}, title = {A FEW COMMENTS ON MATLIS DUALITY}, key = {cite}, author = {Mahmood, Waqas} } APA Mahmood, W . (2014). A FEW COMMENTS ON MATLIS DUALITY. International Electronic Journal of Algebra, 15 (15), 66-76. DOI: 10.24330/ieja.266238 MLA Mahmood, W . "A FEW COMMENTS ON MATLIS DUALITY". International Electronic Journal of Algebra 15 (2014): 66-76 Chicago Mahmood, W . "A FEW COMMENTS ON MATLIS DUALITY". International Electronic Journal of Algebra 15 (2014): 66-76 RIS TY - JOUR T1 - A FEW COMMENTS ON MATLIS DUALITY AU - Waqas Mahmood Y1 - 2014 PY - 2014 N1 - doi: 10.24330/ieja.266238 DO - 10.24330/ieja.266238 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 66 EP - 76 VL - 15 IS - 15 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.266238 UR - https://doi.org/10.24330/ieja.266238 Y2 - 2019 ER - EndNote %0 International Electronic Journal of Algebra A FEW COMMENTS ON MATLIS DUALITY %A Waqas Mahmood %T A FEW COMMENTS ON MATLIS DUALITY %D 2014 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 15 %N 15 %R doi: 10.24330/ieja.266238 %U 10.24330/ieja.266238 ISNAD Mahmood, Waqas . "A FEW COMMENTS ON MATLIS DUALITY". International Electronic Journal of Algebra 15 / 15 (June 2014): 66-76. https://doi.org/10.24330/ieja.266238