Volume 9, Issue 4 (12-2023)                   mmr 2023, 9(4): 111-121 | Back to browse issues page

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Bagherpoor M, Taherizadeh A. Trace ideals and maximal Cohen-Macaulay modules over a Gorenstein local ring. mmr 2023; 9 (4) :111-121
URL: http://mmr.khu.ac.ir/article-1-3304-en.html
1- Kharazmi University, Tehran. Iran , bagherpour.mohammad.2019@gmail.com
2- Kharazmi University, Tehran. Iran
Abstract:   (365 Views)
     All rings throughout this paper are commutative and Noetherian. Semidualizing modules were studied independently by Foxby [4], Golod [5], and Vasconcelos [11]. A finite R-module C is called semidualizing if the natural homothety map is an isomorphism and for all . If a semidualizing R-module has finite injective dimension, it is called dualizing and is denoted by D. The ring itself is an example of a semidualizing R-module. Many researchers, in particular Sather-Wagstaff [12], have studied the semidualizing modules.
     Let M be an R-module. The trace ideal of M, denoted by , is the sum of images of all homomorphisms from M to R. Trace ideals have attracted the attention of many researchers in recent years. In particular, Herzog et al. [6] and Dao et al. [3] studied the trace ideals of canonical modules. Also, the trace ideals of semidualizing modules were studied in [1].  
     In this paper, we study the trace ideals of tensor product of two arbitrary modules. We prove some known facts with a different approach via trace ideals. For example, let C and be two semidualizing R-modules. We show that is projective if and only if C and  are projective R-modules of rank 1. Also, we study the trace ideals of maximal Cohen-Macaulay modules over a Gorenstein local ring.

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Type of Study: Original Manuscript | Subject: alg
Received: 2022/11/28 | Revised: 2024/04/7 | Accepted: 2023/04/4 | Published: 2024/02/17 | ePublished: 2024/02/17

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