期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2006
卷号：2006
DOI：10.1155/IJMMS/2006/72589
出版社：Hindawi Publishing Corporation
摘要：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 xt∈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 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.”
