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...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/8069104 |
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| _version_ | 1832565413160943616 |
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| author | Włodzimierz Fechner Andrzej Olbryś |
| author_facet | Włodzimierz Fechner Andrzej Olbryś |
| author_sort | Włodzimierz Fechner |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-f03d25aa911c41e99b5c6833d8ca7a23 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-f03d25aa911c41e99b5c6833d8ca7a232025-02-03T01:07:58ZengWileyJournal 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 |
| spellingShingle | Włodzimierz Fechner Andrzej Olbryś Systems of Inequalities Characterizing Ring Homomorphisms Journal of Function Spaces |
| title | 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_short | Systems of Inequalities Characterizing Ring Homomorphisms |
| title_sort | systems of inequalities characterizing ring homomorphisms |
| url | http://dx.doi.org/10.1155/2016/8069104 |
| work_keys_str_mv | AT włodzimierzfechner systemsofinequalitiescharacterizingringhomomorphisms AT andrzejolbrys systemsofinequalitiescharacterizingringhomomorphisms |