The uniform symbolic topology property for diagonally \(F\)-regular algebras. (English) Zbl 1444.13001
Let \(R\) be a finite-dimensional Noetherian ring. One of the most interesting questions in recent decades was to find rings satisfy \(p^{(hn)} \subset p^n\) for all \(n\in\mathbb{N}\) for all prime ideals \(p\subset R\) and for some \(h\) independent of \(p\), where \(p^{(m)}\) denotes the \(m\)-th symbolic power of \(p\). Rings for which this number \(h\) can be taken independently of \(p\) (i.e. for which there exists a uniform bound on \(h\) for all \(p\)) are said to have the Uniform Symbolic Topology Property, or USTP for short. In the case of regular rings the problem understood well. In the paper under review, the authors consider the aforementioned problem in the strongly \(F\)-regular case which is weakening of regularity defined for rings of positive characteristic.
Reviewer: Majid Eghbali (Tehran)
MSC:
| 13A15 | Ideals and multiplicative ideal theory in commutative rings |
| 13A35 | Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure |
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