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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| author | Ahmed Ayache David E. Dobbs Othman Echi |
| author_facet | Ahmed Ayache David E. Dobbs Othman Echi |
| author_sort | Ahmed Ayache |
| collection | DOAJ |
| description | 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.” |
| format | Article |
| id | doaj-art-89b9d62cb7134c6580c0b3905f2ac776 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-89b9d62cb7134c6580c0b3905f2ac7762025-02-03T06:12:33ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/7258972589Universal mapping properties of some pseudovaluation domains and related quasilocal domainsAhmed Ayache0David E. Dobbs1Othman Echi2Department of Mathematics, Faculty of Sciences, University of Bahrain, P.O. Box 32038, Isa Town, BahrainDepartment of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, USADepartment of Mathematics, Faculty of Sciences of Tunis, University Tunis-El Manar, Campus Universitaire, Tunis 2092, TunisiaIf (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.”http://dx.doi.org/10.1155/IJMMS/2006/72589 |
| spellingShingle | 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 |
| title | Universal mapping properties of some pseudovaluation domains and related quasilocal domains |
| title_full | Universal mapping properties of some pseudovaluation domains and related quasilocal domains |
| title_fullStr | Universal mapping properties of some pseudovaluation domains and related quasilocal domains |
| title_full_unstemmed | Universal mapping properties of some pseudovaluation domains and related quasilocal domains |
| title_short | Universal mapping properties of some pseudovaluation domains and related quasilocal domains |
| title_sort | universal mapping properties of some pseudovaluation domains and related quasilocal domains |
| url | http://dx.doi.org/10.1155/IJMMS/2006/72589 |
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