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UNIQUE FACTORIZATION RINGS
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UNSPECIFIED (1992) UNIQUE FACTORIZATION RINGS. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 35 (Part 2). pp. 255-269. ISSN 0013-0915.
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Abstract
Let R be a ring. An element p of R is a prime element if pR = Rp is a prime ideal of R. A prime ring R is said to be a Unique Factorisation Ring if every non-zero prime ideal contains a prime element. This paper develops the basic theory of U.F.R.s. We show that every polynomial extension in central indeterminates of a U.F.R. is a U.F.R. We consider in more detail the case when a U.F.R. is either Noetherian or satisfies a polynomial identity. In particular we show that such a ring R is a maximal order, that every height-1 prime ideal of R has a classical localisation in which every two-sided ideal is principal, and that R is the intersection of a left and right Noetherian ring and a simple ring.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | ||||
Publisher: | OXFORD UNIV PRESS UNITED KINGDOM | ||||
ISSN: | 0013-0915 | ||||
Official Date: | June 1992 | ||||
Dates: |
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Volume: | 35 | ||||
Number: | Part 2 | ||||
Number of Pages: | 15 | ||||
Page Range: | pp. 255-269 | ||||
Publication Status: | Published |
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