1
Department of Mathematics, Mahs.C, Islamic Azad University, Mahshahr, Iran
2
Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
3
Department of Mathematics, Imam Khomeini International University, Qazvin, Iran
Abstract
Let $(R,\mathfrak m)$ be a Noetherian local ring, and let $C$ be a semidualizing $R$-module such that $C^{\oplus n}\cong \Hom_R(M,R)$ for some finitely generated $R$-module $M$ and some positive integer $n$. We give conditions on $M$ and $C$ that imply that $C$ is free. In particular, if $R$ is a Cohen-Macaulay local ring of dimension at most one, then $C\cong R$.
Vesalian,R , Taherizadeh,A and Bagheri,M . (2026). Some Freeness Conditions for Semidualizing Modules over Cohen-Macaulay Local Rings. Journal of Applied Mathematics & Data Analytics, 2(2), 10-17.
MLA
Vesalian,R , , Taherizadeh,A , and Bagheri,M . "Some Freeness Conditions for Semidualizing Modules over Cohen-Macaulay Local Rings", Journal of Applied Mathematics & Data Analytics, 2, 2, 2026, 10-17.
HARVARD
Vesalian R, Taherizadeh A, Bagheri M. (2026). 'Some Freeness Conditions for Semidualizing Modules over Cohen-Macaulay Local Rings', Journal of Applied Mathematics & Data Analytics, 2(2), pp. 10-17.
CHICAGO
R Vesalian, A Taherizadeh and M Bagheri, "Some Freeness Conditions for Semidualizing Modules over Cohen-Macaulay Local Rings," Journal of Applied Mathematics & Data Analytics, 2 2 (2026): 10-17,
VANCOUVER
Vesalian R, Taherizadeh A, Bagheri M. Some Freeness Conditions for Semidualizing Modules over Cohen-Macaulay Local Rings. JAMDA. 2026;2(2):10-17.
