University of Guilan Journal of Algebra and Related Topics 2345-3931 14 Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024). 2026 04 01 Identification Gorenstein rings via special semidualizing modules 257 265 8851 10.22124/jart.2025.28567.1720 EN M. Bagheri Department of ‎Mathematics,‎‎ Imam Khomeini ‎‏‎I‎nternational University, Qazvin, Iran A. J. Taherizadeh Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran R. Vesalian Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran Journal Article 2024 09 30 ‎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. https://jart.guilan.ac.ir/article_8851_bddae1840579fd5475d0cdb4194d35ef.pdf