Let $(R, {\frak m})$ be a Noetherian local ring and $M$ be a finitely generated $R$-module such that ${\rm Hom}_R(M,R) \cong \underset{i=1}{\overset{n}{\oplus}} C$ for some positive integer $n$. We try to present new characterizations of Gorenstein rings via $M$ and $C$. It is proved that if ${\rm depth}\, R=0$ and ${\rm id}_R (M) < \infty$ then $R$ is Gorenstein. Also, it is shown that if $M$ is a Cohen-Macaulay $R$-module with finite injective dimension, then $R$ is Gorenstein.
Vesalian, R. , Taherizadeh, A. J. and Bagheri, M. (2025). Identification Gorenstein rings via special semidualizing modules. Journal of Algebra and Related Topics, (), -. doi: 10.22124/jart.2025.28567.1720
MLA
Vesalian, R. , , Taherizadeh, A. J., and Bagheri, M. . "Identification Gorenstein rings via special semidualizing modules", Journal of Algebra and Related Topics, , , 2025, -. doi: 10.22124/jart.2025.28567.1720
HARVARD
Vesalian, R., Taherizadeh, A. J., Bagheri, M. (2025). 'Identification Gorenstein rings via special semidualizing modules', Journal of Algebra and Related Topics, (), pp. -. doi: 10.22124/jart.2025.28567.1720
CHICAGO
R. Vesalian , A. J. Taherizadeh and M. Bagheri, "Identification Gorenstein rings via special semidualizing modules," Journal of Algebra and Related Topics, (2025): -, doi: 10.22124/jart.2025.28567.1720
VANCOUVER
Vesalian, R., Taherizadeh, A. J., Bagheri, M. Identification Gorenstein rings via special semidualizing modules. Journal of Algebra and Related Topics, 2025; (): -. doi: 10.22124/jart.2025.28567.1720
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