SFT-stability and Krull dimension in power series rings over an almost pseudo-valuation domain |
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Authors: | Mohamed Khalifa Ali Benhissi |
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Institution: | 1. Department of Mathematics, Faculty of Sciences of Monastir, 5000, Monastir, Tunisia
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Abstract: | Let \(R\) be an APVD with maximal ideal \(M\) . We show that the power series ring \(Rx_1,\ldots ,x_n]]\) is an SFT-ring if and only if the integral closure of \(R\) is an SFT-ring if and only if ( \(R\) is an SFT-ring and \(M\) is a Noether strongly primary ideal of \((M:M)\) ). We deduce that if \(R\) is an \(m\) -dimensional APVD that is a residually *-domain, then dim \(Rx_1,\ldots ,x_n]]\,=\,nm+1\) or \(nm+n\) . |
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