Multiplication-Like Modules
محورهای موضوعی : مجله بین المللی ریاضیات صنعتی
M. Ahmadi
1
(Department of Mathematics, University of Hormozgan, Bandar Abbas, Hormozgan, Iran.)
J. Moghaderi
2
(Department of Mathematics, University of Hormozgan, Bandar Abbas, Hormozgan, Iran.)
کلید واژه: Free modules, Multiplication-like modules, Multiplication modules, Flat modules, Faithfully flat modules,
چکیده مقاله :
In this paper we introduce the concept of multiplication-like modules and we obtain some related results. We show that an R-module M is multiplication-like if and only if for each ideal I of R, I = (IM :R M). We prove that any multiplication-like module is faithful and r-multiplication. So we get that any flat and multiplication-like module is faithfully flat.
در این مقاله مفهوم مدول­های شبیه-ضربی را معرفی کرده و برخی خواص آنها را بدست می آوریم. نشان می دهیم که R-مدول M، شبیه-ضربی است اگر و تنها اگر برای هر ایده آل I از R داشته باشیم I = (IM :R M). ثابت می کنیم که هر مدول شبیه-ضربی، وفادار و r-ضربی است. همچنین بدست می آوریم که هر مدول وفادار شبیه-ضربی، هموار وفادار است. .
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