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Identification Gorenstein rings via special semidualizing modules | ||
| Journal of Algebra and Related Topics | ||
| دوره 14، S1، تیر 2026، صفحه 257-265 اصل مقاله (153.52 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2025.28567.1720 | ||
| نویسندگان | ||
| M. Bagheri1؛ A. J. Taherizadeh2؛ R. Vesalian* 2 | ||
| 1Department of Mathematics, Imam Khomeini International University, Qazvin, Iran | ||
| 2Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| The Auslander-Reiten conjecture؛ Semidualizing modules؛ Free modules | ||
| مراجع | ||
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[1] M. Bagheri and A. Taherizadeh, On the freeness of dual semidualizing modules, Comm. in Algebra, (1) 50 (2022), 73–81. [2] M. P. Brodmann and R. Y. Sharp, Local Cohomology: An Algebraic Introduction with Geometric Applications, Second edition, Cambridge University Press, 2013. [3] W. Bruns and J. Herzog, Cohen-Macaulay Rings, Revised edition, Cambridge University Press, Cambridge, 1993. [4] L. W. Christensen, Gorenstein dimensions, Lecture Notes in Math., Springer, Berlin, 2000. [5] S. Goto and R. Takahashi, On the Auslander-Reiten conjecture for Cohen-Macaulay local rings, Proc. Amer. Math. Soc., (8) 145 (2017), 3289–3296. [6] H. Matsumura, Commutative ring theory, Cambridge University Press, Cambridge, 1987. [7] J. J. Rotman, An Introduction to Homological Algebra, Second Edition, Springer, New York, 2009. [8] S. Sather-Wagstaff, Semidualizing modules, http://ssather.people.clemson.edu/DOCS/sdm.pdf | ||
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آمار تعداد مشاهده مقاله: 324 تعداد دریافت فایل اصل مقاله: 173 |
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