Localisations dans les ordres maximaux

Chamarie, Marc

doi:10.1080/00927877408822013

Cited by 14 publications

(3 citation statements)

References 6 publications

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“…Because p is a regular element of R it is easy to show that I = pl. (3). Suppose that xa = p"b for some a, beR for and positive integer n. Because xeC(p"R) it follows that aep"R. Hence xaexp"R and the result follows easily.…”

Section: General Theorymentioning

confidence: 76%

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Unique factorisation rings

Chatters

Gilchrist

Wilson

1992

Proceedings of the Edinburgh Mathematical Society

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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.

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Section: General Theorymentioning

confidence: 76%

“…(3) By (2) and Lemma 3.1 (2) there are non-associate prime elements Pi,...,p n of R and non-negative integers a(i) such that xR = pf 1) p" 2 (2) ...p°l n) R. Set y=p 2 {2) pf 3) ...p a n in) . Proof.…”

Section: General Theorymentioning

confidence: 99%

Unique factorisation rings

Chatters

Gilchrist

Wilson

1992

Proceedings of the Edinburgh Mathematical Society

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show abstract

“…C'est l'algebre engendree sur K par n generateurs Y x ,...,Y n soumis aux relations Y t Yj = X^Y^ pour 1 < i, j < n. On a alors: [Y n ; a n ], ou pour 2 < i < n, Gj est l'automorphisme completement premiers V iwj pour (i, j) e I x J. L'automorphisme associe a l'element normal regulier y,y 3 …”

Section: Facteurs Premiers Des Espaces Quantiques Uniparametresunclassified