Bounded Factorization Rings |
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| Authors: | D. D. Anderson Amit Ganatra |
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| Affiliation: | 1. Department of Mathematics , The University of Iowa , Iowa City, Iowa, USA dan-anderson@uiowa.edu;3. Goldman Sachs , New York, New York, USA |
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| Abstract: | In this article we present some results about bounded factorization rings (BFRs), i.e., commutative rings with the property that each nonzero nonunit has a bound on the length of its factorizations into nonunits. In their article Factorization in Commutative Rings with Zero Divisors, Anderson and Valdes-Leon conjectured that R[x], the polynomial ring over R, is a bounded factorization ring if and only if R is a BFR and 0 is primary in R. We give some conditions under which the conjecture is true and present a bounded factorization ring with 0 primary where the polynomial ring is not a BFR. |
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| Keywords: | Bounded factorization ring |
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