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, Volume 17, Issue 1, pp 55–66 | Cite as

Semirigid GCD domains

  • Muhammad Zafrullah


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.


Number Theory Algebraic Geometry Topological Group Integral Domain Unique Factorization 
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Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Muhammad Zafrullah
    • 1
  1. 1.Department of MathematicsUMISTManchesterUK

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