caa a22 4500 606244425 CHVBK 20210128101330.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s12044-015-0218-7 doi (NATIONALLICENCE)springer-10.1007/s12044-015-0218-7 Reflexive modules with finite Gorenstein dimension with respect to a semidualizing module [Elektronische Daten] [Elham Tavasoli, Maryam Salimi, Siamak Yassemi] Let R be a commutative Noetherian ring and let C be a semidualizing R-module. It is shown that a finitely generated R-module M with finite G C -dimension is C-reflexive if and only if M 𝔭 $M_{\mathfrak {p}}$ is C 𝔭 $C_{\mathfrak {p}}$ -reflexive for 𝔭 ∈ Spec ( R ) $\mathfrak {p} \in \text {Spec}\,(R) $ with depth ( R 𝔭 ) ≤ 1 $\text {depth}\,(R_{\mathfrak {p}}) \leq 1$ , and G C 𝔭 − dim R 𝔭 ( M 𝔭 ) ≤ depth ( R 𝔭 ) − 2 $G_{C_{\mathfrak {p}}}-\dim _{R_{\mathfrak {p}}} (M_{\mathfrak {p}}) \leq \text {depth}\,(R_{\mathfrak {p}})-2 $ for 𝔭 ∈ Spec ( R ) $\mathfrak {p} \in \text {Spec}\, (R) $ with depth ( R 𝔭 ) ≥ 2 $\text {depth}\,(R_{\mathfrak {p}})\geq 2 $ . As the ring R itself is a semidualizing module, this result gives a generalization of a natural setting for extension of results due to Serre and Samuel (see Czech. Math. J. 62(3) (9) 663-672 and Beiträge Algebra Geom. 50(2) (3) 353-362). In addition, it is shown that over ring R with dim R ≤ n $\dim R \leq n$ , where n≥2 is an integer, G D − dim R ( Hom R ( M , D ) ) ≤ n − 2 $G_{D}-\dim _{R} (\text {Hom}\,_{R} (M,D)) \leq n-2$ for every finitely generated R-module M and a dualizing R-module D. Indian Academy of Sciences, 2015 Semidualizing nationallicence totally C -reflexive nationallicence dualizing nationallicence G C -dimension nationallicence Tavasoli Elham Department of Mathematics, East Tehran Branch, Islamic Azad University, Tehran, Iran aut Salimi Maryam Department of Mathematics, East Tehran Branch, Islamic Azad University, Tehran, Iran aut Yassemi Siamak Department of Mathematics, University of Tehran, Tehran, Iran aut Proceedings - Mathematical Sciences Springer India 125/1(2015-02-01), 21-28 0253-4142 125:1<21 2015 125 12044 https://doi.org/10.1007/s12044-015-0218-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s12044-015-0218-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Tavasoli Elham Department of Mathematics, East Tehran Branch, Islamic Azad University, Tehran, Iran aut NATIONALLICENCE 700 1- Salimi Maryam Department of Mathematics, East Tehran Branch, Islamic Azad University, Tehran, Iran aut NATIONALLICENCE 700 1- Yassemi Siamak Department of Mathematics, University of Tehran, Tehran, Iran aut NATIONALLICENCE 773 0- Proceedings - Mathematical Sciences Springer India 125/1(2015-02-01), 21-28 0253-4142 125:1<21 2015 125 12044