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
If and are quasilocal (commutative integral) domains and is a (unital) ring homomorphism, then is said to be a strong local homomorphism (resp., radical local homomorphism) if (resp., and for each , there exists a positive integer such that ). It is known that if is a strong local homomorphism where is a pseudovaluation domain that is not a field and is a valuation domain that is not a field, then factors via a unique strong local homomorphism through the inclusion map from to its canonically associated valuation overring . Analogues of this result are obtained which delete the conditions that and are not fields, thus obtaining new characterizations of when 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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