On Presented Dimensions of Modules and Rings

On Presented Dimensions of Modules and Rings

We define the presented dimensions for modules and rings to measure how far away a module is from having an infinite finite presentation and develop ways to compute the projective dimension of a module with a finite presented dimension and the right global dimension of a ring. We also make a compari...

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Bibliographic Details
Main Authors: Dexu Zhou, Zhiwei Gong
Format: Article
Language:English
Published: Hindawi Limited 2010-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2010/256267
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spelling doaj-23d9fdcc2da347129d4b1a67c98c74722020-11-24T22:01:19ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252010-01-01201010.1155/2010/256267256267On Presented Dimensions of Modules and RingsDexu Zhou0Zhiwei Gong1Department of Mathematics, Fujian Normal University, Fuzhou 350007, ChinaCollege of Computer and Information, Fujian Agriculture and Forestry University, Fuzhou 350002, ChinaWe define the presented dimensions for modules and rings to measure how far away a module is from having an infinite finite presentation and develop ways to compute the projective dimension of a module with a finite presented dimension and the right global dimension of a ring. We also make a comparison of the right global dimension, the weak global dimension, and the presented dimension and divide rings into four classes according to these dimensions.http://dx.doi.org/10.1155/2010/256267
collection DOAJ
language English
format Article
sources DOAJ
author Dexu Zhou
Zhiwei Gong
spellingShingle Dexu Zhou
Zhiwei Gong
On Presented Dimensions of Modules and Rings
International Journal of Mathematics and Mathematical Sciences
author_facet Dexu Zhou
Zhiwei Gong
author_sort Dexu Zhou
title On Presented Dimensions of Modules and Rings
title_short On Presented Dimensions of Modules and Rings
title_full On Presented Dimensions of Modules and Rings
title_fullStr On Presented Dimensions of Modules and Rings
title_full_unstemmed On Presented Dimensions of Modules and Rings
title_sort on presented dimensions of modules and rings
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2010-01-01
description We define the presented dimensions for modules and rings to measure how far away a module is from having an infinite finite presentation and develop ways to compute the projective dimension of a module with a finite presented dimension and the right global dimension of a ring. We also make a comparison of the right global dimension, the weak global dimension, and the presented dimension and divide rings into four classes according to these dimensions.
url http://dx.doi.org/10.1155/2010/256267
work_keys_str_mv AT dexuzhou onpresenteddimensionsofmodulesandrings
AT zhiweigong onpresenteddimensionsofmodulesandrings
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