On Rings Whose Reflexive Ideals are Principal |
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Authors: | Evrim Akalan |
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Institution: | 1. Mathematics Department , Hacettepe University , Ankara, Turkey eakalan@hacettepe.edu.tr |
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Abstract: | We call a prime Noetherian maximal order R a pseudo-principal ring if every reflexive ideal of R is principal. This class of rings is a broad class properly containing both prime Noetherian pri-(pli) rings and Noetherian unique factorization rings (UFRs). We show that the class of pseudo-principal rings is closed under formation of n × n full matrix rings. Moreover, we prove that if R is a pseudo-principal ring, then the polynomial ring Rx] is also a pseudo-principal ring. We provide examples to illustrate our results. |
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Keywords: | Maximal order Principal ideal Pseudo-principal Reflexive ideal |
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