ایده‌آل ‌های اثر و مدول‌ های کوهن - مکالی ماکسیمال روی یک حلقه گرنشتاین

در این مقاله به بررسی ایده‌آل ‌های اثر از ضرب تانسوری دو مدول می‌پردازیم. همچنین برخی از نتایج شناخته شده را به کمک ایده‌آل‌های اثر تعمیم و برای برخی دیگر اثبات جدید ارائه می‌کنیم. علاوه بر این، بررسی ایده‌آل‌های اثر از مدول‌های کوهن-مکالی ماکسیمال روی حلقه‌های گرنشتاین جزو اهداف این مقاله است. 

trace ideals and maximal cohen-macaulay modules over a gorenstein local ring

     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.