کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4584527 1630494 2014 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Simple-direct-injective modules
ترجمه فارسی عنوان
ماژول های ساده مستقیم تزریق
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

A module M over a ring is called simple-direct-injective if, whenever A and B are simple submodules of M   with A≅BA≅B and B⊆⊕MB⊆⊕M, we have A⊆⊕MA⊆⊕M. Various basic properties of these modules are proved, and some well-studied rings are characterized using simple-direct-injective modules. For instance, it is proved that a ring R is artinian serial with Jacobson radical square zero if and only if every simple-direct-injective right R-module is a C3-module, and that a regular ring R is a right V-ring (i.e., every simple right R-module is injective) if and only if every cyclic right R-module is simple-direct-injective. The latter is a new answer to Fisher's question of when regular rings are V-rings [8].

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 420, 15 December 2014, Pages 39–53
نویسندگان
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