Compatible elements in partly ordered groups
Some conditions equivalent to a strong quasi-divisor property (SQDP) for a partly ordered group G are derived. It is proved that if G is defined by a family of t-valuations of finite character, then G admits an SQDP if and only if it admits a quasi-divisor property and any finitely generated t-ideal...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.4041 |
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| _version_ | 1832561633895907328 |
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| author | Jirí Mockor Angeliki Kontolatou |
| author_facet | Jirí Mockor Angeliki Kontolatou |
| author_sort | Jirí Mockor |
| collection | DOAJ |
| description | Some conditions equivalent to a strong quasi-divisor property (SQDP) for a partly ordered group G are derived. It is proved that if G is defined by a family of t-valuations of finite character, then G admits an SQDP if and only if it admits a quasi-divisor property and any finitely generated t-ideal is generated by two elements. A topological density condition in topological group of finitely generated t-ideals and/or compatible elements are proved to be equivalent to SQDP. |
| format | Article |
| id | doaj-art-502becbfe49f4f8fb73d48988b30fe41 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-502becbfe49f4f8fb73d48988b30fe412025-02-03T01:24:31ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005244041404810.1155/IJMMS.2005.4041Compatible elements in partly ordered groupsJirí Mockor0Angeliki Kontolatou1Department of Mathematics, University of Ostrava, Ostrava CZ-702 00, Czech RepublicDepartment of Mathematics, School of Natural Sciences, University of Patras, Patras 26500, GreeceSome conditions equivalent to a strong quasi-divisor property (SQDP) for a partly ordered group G are derived. It is proved that if G is defined by a family of t-valuations of finite character, then G admits an SQDP if and only if it admits a quasi-divisor property and any finitely generated t-ideal is generated by two elements. A topological density condition in topological group of finitely generated t-ideals and/or compatible elements are proved to be equivalent to SQDP.http://dx.doi.org/10.1155/IJMMS.2005.4041 |
| spellingShingle | Jirí Mockor Angeliki Kontolatou Compatible elements in partly ordered groups International Journal of Mathematics and Mathematical Sciences |
| title | Compatible elements in partly ordered groups |
| title_full | Compatible elements in partly ordered groups |
| title_fullStr | Compatible elements in partly ordered groups |
| title_full_unstemmed | Compatible elements in partly ordered groups |
| title_short | Compatible elements in partly ordered groups |
| title_sort | compatible elements in partly ordered groups |
| url | http://dx.doi.org/10.1155/IJMMS.2005.4041 |
| work_keys_str_mv | AT jirimockor compatibleelementsinpartlyorderedgroups AT angelikikontolatou compatibleelementsinpartlyorderedgroups |