A Characterization of Left Regularity
We show that a zero-symmetric near-ring $N$ is left regular if and only if $N $ is regular and isomorphic to a subdirect product of integral near-rings, where each component is either an Anshel-Clay near-ring or a trivial integral near-ring. We also show that a zero-symmetric near-ring is regular wi...
| Main Author: | |
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| Format: | Article |
| Language: | English |
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Emrah Evren KARA
2019-03-01
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| Series: | Universal Journal of Mathematics and Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/675282 |
| _version_ | 1797350215526645760 |
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| author | Peter Fuchs |
| author_facet | Peter Fuchs |
| author_sort | Peter Fuchs |
| collection | DOAJ |
| description | We show that a zero-symmetric near-ring $N$ is left regular if and only if $N $ is regular and isomorphic to a subdirect product of integral near-rings, where each component is either an Anshel-Clay near-ring or a trivial integral near-ring. We also show that a zero-symmetric near-ring is regular without nonzero nilpotent elements if and only if the multiplicative semigroup of N is a union of disjoint groups. |
| first_indexed | 2024-03-08T12:41:29Z |
| format | Article |
| id | doaj.art-8dd1d19c983d4e9daf8bd13f0e2df6ae |
| institution | Directory Open Access Journal |
| issn | 2619-9653 |
| language | English |
| last_indexed | 2024-03-08T12:41:29Z |
| publishDate | 2019-03-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Universal Journal of Mathematics and Applications |
| spelling | doaj.art-8dd1d19c983d4e9daf8bd13f0e2df6ae2024-01-21T10:06:59ZengEmrah Evren KARAUniversal Journal of Mathematics and Applications2619-96532019-03-0121111310.32323/ujma.4697451225A Characterization of Left RegularityPeter Fuchs0Johannes Kepler University, Altenbergerstrasse 69, A-4040 Linz, AustriaWe show that a zero-symmetric near-ring $N$ is left regular if and only if $N $ is regular and isomorphic to a subdirect product of integral near-rings, where each component is either an Anshel-Clay near-ring or a trivial integral near-ring. We also show that a zero-symmetric near-ring is regular without nonzero nilpotent elements if and only if the multiplicative semigroup of N is a union of disjoint groups.https://dergipark.org.tr/tr/download/article-file/675282anshel-clay near-ringintegral near-ringleft regularregular |
| spellingShingle | Peter Fuchs A Characterization of Left Regularity Universal Journal of Mathematics and Applications anshel-clay near-ring integral near-ring left regular regular |
| title | A Characterization of Left Regularity |
| title_full | A Characterization of Left Regularity |
| title_fullStr | A Characterization of Left Regularity |
| title_full_unstemmed | A Characterization of Left Regularity |
| title_short | A Characterization of Left Regularity |
| title_sort | characterization of left regularity |
| topic | anshel-clay near-ring integral near-ring left regular regular |
| url | https://dergipark.org.tr/tr/download/article-file/675282 |
| work_keys_str_mv | AT peterfuchs acharacterizationofleftregularity AT peterfuchs characterizationofleftregularity |