Ideals and free Pairs in the semigroup β ℤ
We prove that the equations ξ+x=mξ+y, x+ξ=y+mξ have no solutions in the semigroup β ℤ for every free ultrafilter ξ and every integer m∈0, 1. We study semigroups generated by the ultrafilters ξ, mξ. For left maximal idempotents, we prove a reduced hypothesis about elements of finite order in β ℤ....
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| Datum: | 1997 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1997
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5033 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511228638527488 |
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| author | Protasov, I. V. Протасов, И. В. Протасов, И. В. |
| author_facet | Protasov, I. V. Протасов, И. В. Протасов, И. В. |
| author_sort | Protasov, I. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:23:18Z |
| description | We prove that the equations ξ+x=mξ+y, x+ξ=y+mξ have no solutions in the semigroup β ℤ for every free ultrafilter ξ and every integer m∈0, 1. We study semigroups generated by the ultrafilters ξ, mξ. For left maximal idempotents, we prove a reduced hypothesis about elements of finite order in β ℤ. |
| first_indexed | 2026-03-24T03:09:34Z |
| format | Article |
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| id | umjimathkievua-article-5033 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:09:34Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/a5/012995bb10de8144ec73a0e9bfd0d1a5.pdf |
| spelling | umjimathkievua-article-50332020-03-18T21:23:18Z Ideals and free Pairs in the semigroup β ℤ Идеалы и свободные пары в полугруппе β ℤ Protasov, I. V. Протасов, И. В. Протасов, И. В. We prove that the equations ξ+x=mξ+y, x+ξ=y+mξ have no solutions in the semigroup β ℤ for every free ultrafilter ξ and every integer m∈0, 1. We study semigroups generated by the ultrafilters ξ, mξ. For left maximal idempotents, we prove a reduced hypothesis about elements of finite order in β ℤ. Доведено, що рівняння ξ+x=mξ+y, x+ξ=y+mξ не мають розв'язків у півгрупі β ℤ для кожного вільного ультрафільтра ξ і кожного цілого числа m∈0, 1. Вивчаються півгрупи, породжені ультрафільтрами ξ, mξ. Для лівомаксимальиих ідемпотентів доведена редукована гіпотеза про елементи скінченного порядку в β ℤ. Institute of Mathematics, NAS of Ukraine 1997-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5033 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 4 (1997); 573–580 Український математичний журнал; Том 49 № 4 (1997); 573–580 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5033/6765 https://umj.imath.kiev.ua/index.php/umj/article/view/5033/6766 Copyright (c) 1997 Protasov I. V. |
| spellingShingle | Protasov, I. V. Протасов, И. В. Протасов, И. В. Ideals and free Pairs in the semigroup β ℤ |
| title | Ideals and free Pairs in the semigroup β ℤ |
| title_alt | Идеалы и свободные пары в полугруппе β ℤ |
| title_full | Ideals and free Pairs in the semigroup β ℤ |
| title_fullStr | Ideals and free Pairs in the semigroup β ℤ |
| title_full_unstemmed | Ideals and free Pairs in the semigroup β ℤ |
| title_short | Ideals and free Pairs in the semigroup β ℤ |
| title_sort | ideals and free pairs in the semigroup β ℤ |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5033 |
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