International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2006 / Article

Open Access

Volume 2006 |Article ID 072589 | https://doi.org/10.1155/IJMMS/2006/72589

Ahmed Ayache, David E. Dobbs, Othman Echi, "Universal mapping properties of some pseudovaluation domains and related quasilocal domains", International Journal of Mathematics and Mathematical Sciences, vol. 2006, Article ID 072589, 12 pages, 2006. https://doi.org/10.1155/IJMMS/2006/72589

Universal mapping properties of some pseudovaluation domains and related quasilocal domains

Received24 Jan 2005
Revised05 Jan 2006
Accepted22 Jan 2006
Published18 May 2006

Abstract

If (R,M) and (S,N) are quasilocal (commutative integral) domains and f:RS 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 xN, there exists a positive integer t such that xtf(M)). It is known that if f:RS 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 iR 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 iR 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.”

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Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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