Global dimension of rings with krull dimension
作者:
John J. Koker,
期刊:
Communications in Algebra
(Taylor Available online 1992)
卷期:
Volume 20,
issue 10
页码: 2863-2876
ISSN:0092-7872
年代: 1992
DOI:10.1080/00927879208824494
出版商: Marcel Dekker, Inc.
数据来源: Taylor
摘要:
The left global dimension of a semiprime ring, with left Krull dimension α≥1 is found to be the supremum of the projective dimensions of the p-critical cyclic modules where β≤α. A similar result is true for upper triangular matrix rings whose entries come from a domain with Krull dimension. In addition if R is a a ring of the formwhere S is a semiprime ring with left Krull dimension α≥1, T is any ring with l.K dim T≤α, and A is an S-T bimodule such that sA has Krull dimension then the left global dimension of R is the supremum of the projective dimensions of the -critical cyclic left R-modules where β<αa. These results are used to compute homological dimensions of rings with Krull dimension. Some analogues are given for weak dimension and for rings with Gabriel dimension.
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