Abstract
Let R be a commutative integral domain. An element x of R is calledrigid if for all r,s dividing x; r divides s or s divides r. In our terminology, R issemirigid if each non zero non unit of R is a finite product of rigid elements. We show that semirigid GCD domains have a type of unique factorization, and are a known generalization of Krull domains.
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Basic ideas are taken from the author's Doctoral Thesis submitted to the University of London in 1974.
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Zafrullah, M. Semirigid GCD domains. Manuscripta Math 17, 55–66 (1975). https://doi.org/10.1007/BF01154282
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DOI: https://doi.org/10.1007/BF01154282