Abstract
Let R be a commutative integral domain with 1. The non-zero elements a,b of R may be calledv-coprime if aR∩bR=abR. A Krull domain is calledalmost factorial if for all f,g in R there is n∈N such that fnR∩gnR is principal. From this it is easy to establish that if R is almost factorial then for all x in R there is n∈N such that xn=p1p2...pr where pi are mutually v-coprime primary elements and that this expression is unique. In this article we drop the requirement that R be Krull and replace the primary elements by elements calledprime blocks and develope a theory of almost factoriality, a special case of which is the theory of almost factorial Krull domains.
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Zafrullah, M. A general theory of almost factoriality. Manuscripta Math 51, 29–62 (1985). https://doi.org/10.1007/BF01168346
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DOI: https://doi.org/10.1007/BF01168346