Some remarks on \(S\)-valuation domains. (English) Zbl 1541.13018
All rings considered in this paper are commutative with identity. The authors define in this paper the notion of \(S\)-valuation domains in the following way: let \(A\) be a an integral domain and \(S\) a multiplicative subset of \(A.\) The ring \(A\) is called \(S\)-valuation if for every ideals \(I\) and \(J\) of \(A\) there exists \(s\in S\) such that \(sI\subset J\) or \(sJ\subset I. \) Many properties of \(S\)-valuation domains are then given.
Reviewer: Sana Hizem (Monastir)
MSC:
| 13E05 | Commutative Noetherian rings and modules |
| 13A15 | Ideals and multiplicative ideal theory in commutative rings |
References:
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