کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4584677 1630498 2014 33 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Reconstructing projective modules from its trace ideal
ترجمه فارسی عنوان
بازسازی ماژول های تصویری از ایده آل های ردیابی آن
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

We make a detailed study of idempotent ideals that are traces of countably generated projective right modules. We associate to such ideals an ascending chain of finitely generated left ideals and, dually, a descending chain of cofinitely generated right ideals.The study of the first sequence allows us to characterize trace ideals of projective modules and to show that projective modules can always be lifted modulo the trace ideal of a projective module. As a consequence we give some new classification results of (countably generated) projective modules over particular classes of semilocal rings. The study of the second sequence leads us to consider projective modules over noetherian FCR-algebras; we make some constructions of non-trivial projective modules showing that over such rings the behavior of countably generated projective modules that are not direct sum of finitely generated ones is, in general, quite complex.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 416, 15 October 2014, Pages 25–57
نویسندگان
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