Abstract.
We investigate factorization in a nonzero integral domain A without identity. Now A may be viewed as a proper ideal of an integral domain D with identity having the same quotient field as A where \(A[1] \subseteq D \subseteq A:A\). We study the relationship between factorization in A and D, especially in the case where D = A[1] or A:A. Particular interest is given to various notions of unique factorization in A and to the relationship between A or D being atomic, satisfying ACCP, or being a bounded factorization domain, half-factorial domain, or finite factorization domain.
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Received: June 24, 2008. Revised: March 26, 2009.
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Anderson, D.D., Preisser, J. Factorization in Integral Domains without Identity. Results. Math. 55, 249 (2009). https://doi.org/10.1007/s00025-009-0405-x
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DOI: https://doi.org/10.1007/s00025-009-0405-x