کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6414758 | 1630515 | 2014 | 10 صفحه PDF | دانلود رایگان |
Until now there has been no suitable dimension to measure how far a module deviates from being uniserial. We define and study a new dimension, which we call uniserial dimension. The uniserial dimension is a measure of how far a module deviates from being uniserial. It is shown that for a ring R and an ordinal number α, there exists an R-module of uniserial dimension α. We show that a commutative ring R is Noetherian (resp. Artinian) if and only if every finitely generated R-module has (resp. finite) uniserial dimension. We characterize rings whose modules have uniserial dimension. In fact, it is shown that every right R-module has uniserial dimension if and only if the free right R-module â¨i=1âR has uniserial dimension if and only if R is a semisimple Artinian ring.
Journal: Journal of Algebra - Volume 399, 1 February 2014, Pages 894-903