کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9493550 1334248 2005 28 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Dual Krull dimension and quotient finite dimensionality
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Dual Krull dimension and quotient finite dimensionality
چکیده انگلیسی
A modular lattice L with 0 and 1 is called quotient finite dimensional (QFD) if [x,1] has no infinite independent set for any x∈L. We characterize upper continuous modular lattices L that have dual Krull dimension k0(L)⩽α, by relating that with the property of L being QFD and with other conditions involving subdirectly irreducible lattices and/or meet irreducible elements. In particular, we answer in the positive, in the more general latticial setting, some open questions on QFD modules raised by Albu and Rizvi [Comm. Algebra 29 (2001) 1909-1928]. Applications of these results are given to Grothendieck categories and module categories equipped with a torsion theory.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 284, Issue 1, 1 February 2005, Pages 52-79
نویسندگان
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