Abstract
AbstractFor an infinite cardinal ℵ an associative ring R is quotient ℵ<-dimensional if the generalized Goldie dimension of all right quotient modules of RR are strictly less than ℵ. This latter quotient property of RR is characterized in terms of certain essential submodules of cyclic modules being generated by less than ℵ elements, and also in terms of weak injectivity and tightness properties of certain subdirect products of injective modules. The above is the higher cardinal analogue of the known theory in the finite ℵ = ℵ0 case.
Publisher
Cambridge University Press (CUP)
Reference11 articles.
1. Rings whose cyclics have finite Goldie dimension;Al-Huzali;J. Algebra,1990
2. Rings whose cyclic modules have finitely generated socle
3. Krull dimension;Gordon;Memoirs of the Amer. Math. Soc.,1973
4. Module Types
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Classes of Modules;MONOGR TXB PURE APPL;2006-06-19