Power series over strongly Hopfian bounded rings |
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Authors: | Mohamed Khalifa |
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Affiliation: | 1. Department of Mathematics, University of Sousse, Sousse, Tunisiakhalifa.mohamed_cr@yahoo.fr |
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Abstract: | Let R be a commutative ring with identity. We show that R[[X]] is strongly Hopfian bounded if and only if R has a strongly Hopfian bounded extension T such that Ic(T) contains a regular element of T. We deduce that if R[[X]] is strongly Hopfian bounded, then so is R[[X,Y]] where X,Y are two indeterminates over R. Also we show that if R is embeddable in a zero-dimensional strongly Hopfian bounded ring, then so is R[[X]] (this generalizes most results of Hizem [11 Hizem, S. (2011). Formal power series over strongly Hopfian rings. Commun. Algebra 39(1):279–291.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]]). For a chained ring R, we show that R[[X]] is strongly Hopfian if and only if R is strongly Hopfian. |
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Keywords: | Chained ring embeddability in a zero-dimensional ring power series ring SFT-ring strongly Hopfian (bounded) ring |
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