Homomophic images of an infinite product of zero-dimensional rings
作者:
Robert Glimer,
William Heinzer,
期刊:
Communications in Algebra
(Taylor Available online 1995)
卷期:
Volume 23,
issue 5
页码: 1953-1965
ISSN:0092-7872
年代: 1995
DOI:10.1080/00927879508825321
出版商: Marcel Dekker, Inc.
数据来源: Taylor
摘要:
Let R=∏αεAbe an infinite product of zero-dimensionalchained rings. It is known that R is either zero-dimensional or infinitedimensional. We prove that a finite-dimensional homo~norphic image of R is of dimension at most one. If each R, is a PIR and if R is infinite-dimensional, then R admits one-dimensional hornomorphic images. However, without the PIR hypothesis on the rings Rα, we present examples to show that R may be infinite-dimensional while each finite-dimensional homomorphic image of R is zero-dimensicnal. JVe prove that a prime ideal of R of positive height is of infinite height, and we give conditions for an infinite product of zero-dimensional local rings to admit a one-dimensional local domain as a honlomorphic image.
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