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Universal mapping properties of some pseudovaluation domains and related quasilocal domains

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  • Ahmed Ayache
  • David E. Dobbs
  • Othman Echi

Abstract

If ( R , M ) and ( S , N ) are quasilocal (commutative integral) domains and f : R → S is a (unital) ring homomorphism, then f is said to be a strong local homomorphism (resp., radical local homomorphism ) if f ( M ) = N (resp., f ( M ) ⊆ N and for each x ∈ N , there exists a positive integer t such that x t ∈ f ( M ) ). It is known that if f : R → S is a strong local homomorphism where R is a pseudovaluation domain that is not a field and S is a valuation domain that is not a field, then f factors via a unique strong local homomorphism through the inclusion map i R from R to its canonically associated valuation overring ( M : M ) . Analogues of this result are obtained which delete the conditions that R and S are not fields, thus obtaining new characterizations of when i R is integral or radicial. Further analogues are obtained in which the “pseudovaluation domain that is not a field†condition is replaced by the APVDs of Badawi-Houston and the “strong local homomorphism†conditions are replaced by “radical local homomorphism.â€

Suggested Citation

  • Ahmed Ayache & David E. Dobbs & Othman Echi, 2006. "Universal mapping properties of some pseudovaluation domains and related quasilocal domains," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-12, May.
    • Handle: RePEc:hin:jijmms:072589
    DOI: 10.1155/IJMMS/2006/72589
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