Principal filters of some ordered $\Gamma$-semigroups
For an intra-regular or a left regular and left duo ordered $\Gamma$-semigroup $M$, we describe the principal filter of $M$ which plays an essential role in the structure of this type of $po$-$\Gamma$-semigroups. We also prove that an ordered $\Gamma$-semigroup $M$ is intra-regular if and only if t...
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| Language: | English |
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Republic of Armenia National Academy of Sciences
2016-12-01
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| Series: | Armenian Journal of Mathematics |
| Online Access: | http://www.armjmath.sci.am/index.php/ajm/article/view/127 |
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doaj-3a6c8aac35a144e6a448b43873e3318f2020-11-24T21:11:57ZengRepublic of Armenia National Academy of SciencesArmenian Journal of Mathematics1829-11632016-12-0182Principal filters of some ordered $\Gamma$-semigroupsNiovi Kehayopulu0Michael Tsingelis1Department of Mathematics University of Athens 15784 Panepistimiopolis, Athens, GreeceHellenic Open University School of Science and Technology Studies in Natural Sciences, Greece For an intra-regular or a left regular and left duo ordered $\Gamma$-semigroup $M$, we describe the principal filter of $M$ which plays an essential role in the structure of this type of $po$-$\Gamma$-semigroups. We also prove that an ordered $\Gamma$-semigroup $M$ is intra-regular if and only if the ideals of $M$ are semiprime and it is left (right) regular and left (right) duo if and only if the left (right) ideals of $M$ are semiprime. http://www.armjmath.sci.am/index.php/ajm/article/view/127 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Niovi Kehayopulu Michael Tsingelis |
| spellingShingle |
Niovi Kehayopulu Michael Tsingelis Principal filters of some ordered $\Gamma$-semigroups Armenian Journal of Mathematics |
| author_facet |
Niovi Kehayopulu Michael Tsingelis |
| author_sort |
Niovi Kehayopulu |
| title |
Principal filters of some ordered $\Gamma$-semigroups |
| title_short |
Principal filters of some ordered $\Gamma$-semigroups |
| title_full |
Principal filters of some ordered $\Gamma$-semigroups |
| title_fullStr |
Principal filters of some ordered $\Gamma$-semigroups |
| title_full_unstemmed |
Principal filters of some ordered $\Gamma$-semigroups |
| title_sort |
principal filters of some ordered $\gamma$-semigroups |
| publisher |
Republic of Armenia National Academy of Sciences |
| series |
Armenian Journal of Mathematics |
| issn |
1829-1163 |
| publishDate |
2016-12-01 |
| description |
For an intra-regular or a left regular and left duo ordered $\Gamma$-semigroup $M$, we describe the principal filter of $M$ which plays an essential role in the structure of this type of $po$-$\Gamma$-semigroups. We also prove that an ordered $\Gamma$-semigroup $M$ is intra-regular if and only if the ideals of $M$ are semiprime and it is left (right) regular and left (right) duo if and only if the left (right) ideals of $M$ are semiprime.
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| url |
http://www.armjmath.sci.am/index.php/ajm/article/view/127 |
| work_keys_str_mv |
AT niovikehayopulu principalfiltersofsomeorderedgammasemigroups AT michaeltsingelis principalfiltersofsomeorderedgammasemigroups |
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1716752060255305728 |