U-factorization of ideals |
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Authors: | Jason Robert Juett |
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Affiliation: | Department of Mathematics, Texas State University, San Marcos, TX, USA |
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Abstract: | We study the factorization of ideals of a commutative ring, in the context of the U-factorization framework introduced by Fletcher. This leads to several “U-factorability” properties weaker than unique U-factorization. We characterize these notions, determine the implications between them, and give several examples to illustrate the differences. For example, we show that a ring is a general ZPI-ring if and only if its monoid of ideals has unique factorization in the sense of Fletcher. We also examine how these “U-factorability” properties behave with respect to several ring-theoretic constructions. |
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Keywords: | Commutative rings factorization ideals multiplicative ideal theory U-factorization |
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