Universal mapping properties of some pseudovaluation domains and related quasilocal domains
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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/72589 |
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| Summary: | 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.” |
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| ISSN: | 0161-1712 1687-0425 |