Systems of Inequalities Characterizing Ring Homomorphisms
Assume that T:P→R and U:P→R are arbitrary mappings between two partially ordered rings P and R. We study a few systems of functional inequalities which characterize ring homomorphisms. For example, we prove that if T and U satisfy T(f+g)≥T(f)+T(g), U(f·g)≥U(f)·U(g), for all f,g∈P and T≥U, then U=T...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2016-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/8069104 |
| id |
doaj-f03d25aa911c41e99b5c6833d8ca7a23 |
|---|---|
| record_format |
Article |
| spelling |
doaj-f03d25aa911c41e99b5c6833d8ca7a232020-11-25T00:17:40ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/80691048069104Systems of Inequalities Characterizing Ring HomomorphismsWłodzimierz Fechner0Andrzej Olbryś1Institute of Mathematics, Łódź University of Technology, Ul. Wólczańska 215, 93-005 Łódź, PolandInstitute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, PolandAssume that T:P→R and U:P→R are arbitrary mappings between two partially ordered rings P and R. We study a few systems of functional inequalities which characterize ring homomorphisms. For example, we prove that if T and U satisfy T(f+g)≥T(f)+T(g), U(f·g)≥U(f)·U(g), for all f,g∈P and T≥U, then U=T and this mapping is a ring homomorphism. Moreover, we find two other systems for which we obtain analogous assertions.http://dx.doi.org/10.1155/2016/8069104 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Włodzimierz Fechner Andrzej Olbryś |
| spellingShingle |
Włodzimierz Fechner Andrzej Olbryś Systems of Inequalities Characterizing Ring Homomorphisms Journal of Function Spaces |
| author_facet |
Włodzimierz Fechner Andrzej Olbryś |
| author_sort |
Włodzimierz Fechner |
| title |
Systems of Inequalities Characterizing Ring Homomorphisms |
| title_short |
Systems of Inequalities Characterizing Ring Homomorphisms |
| title_full |
Systems of Inequalities Characterizing Ring Homomorphisms |
| title_fullStr |
Systems of Inequalities Characterizing Ring Homomorphisms |
| title_full_unstemmed |
Systems of Inequalities Characterizing Ring Homomorphisms |
| title_sort |
systems of inequalities characterizing ring homomorphisms |
| publisher |
Hindawi Limited |
| series |
Journal of Function Spaces |
| issn |
2314-8896 2314-8888 |
| publishDate |
2016-01-01 |
| description |
Assume that T:P→R and U:P→R are arbitrary mappings between two partially ordered rings P and R. We study a few systems of functional inequalities which characterize ring homomorphisms. For example, we prove that if T and U satisfy T(f+g)≥T(f)+T(g), U(f·g)≥U(f)·U(g), for all f,g∈P and T≥U, then U=T and this mapping is a ring homomorphism. Moreover, we find two other systems for which we obtain analogous assertions. |
| url |
http://dx.doi.org/10.1155/2016/8069104 |
| work_keys_str_mv |
AT włodzimierzfechner systemsofinequalitiescharacterizingringhomomorphisms AT andrzejolbrys systemsofinequalitiescharacterizingringhomomorphisms |
| _version_ |
1725378448136863744 |