On the identities in algebras generated by linearly connected idempotents
We investigate the problem of the existence of polynomial identities (PI) in algebras generated by idempotents whose linear combination is equal to identity. In the case where the number of idempotents is greater than or equal to five, we prove that these algebras are not PI-algebras. In the case of...
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| Дата: | 2004 |
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| Автори: | , , , , , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2004
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/3798 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860509931263754240 |
|---|---|
| author | Rabanovych, V. I. Samoilenko, Yu. S. Strilets, O. V. Рабанович, В. И. Самойленко, Ю. С. Стрелец, А. В. Рабанович, В. И. Самойленко, Ю. С. Стрелец, А. В. |
| author_facet | Rabanovych, V. I. Samoilenko, Yu. S. Strilets, O. V. Рабанович, В. И. Самойленко, Ю. С. Стрелец, А. В. Рабанович, В. И. Самойленко, Ю. С. Стрелец, А. В. |
| author_sort | Rabanovych, V. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:09:24Z |
| description | We investigate the problem of the existence of polynomial identities (PI) in algebras generated by idempotents whose linear combination is equal to identity. In the case where the number of idempotents is greater than or equal to five, we prove that these algebras are not PI-algebras. In the case of four idempotents, in order that an algebra be a PI-algebra, it is necessary and sufficient that the sum of the coefficients of the linear combination be equal to two. In this case, these algebras are F 4-algebras. |
| first_indexed | 2026-03-24T02:48:56Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-3798 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:48:56Z |
| publishDate | 2004 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/4c/06855d2e9ef54353ec3b7c95bb673f4c.pdf |
| spelling | umjimathkievua-article-37982020-03-18T20:09:24Z On the identities in algebras generated by linearly connected idempotents О тождествах в алгебрах, порожденных линейно связанными идемпотептами Rabanovych, V. I. Samoilenko, Yu. S. Strilets, O. V. Рабанович, В. И. Самойленко, Ю. С. Стрелец, А. В. Рабанович, В. И. Самойленко, Ю. С. Стрелец, А. В. We investigate the problem of the existence of polynomial identities (PI) in algebras generated by idempotents whose linear combination is equal to identity. In the case where the number of idempotents is greater than or equal to five, we prove that these algebras are not PI-algebras. In the case of four idempotents, in order that an algebra be a PI-algebra, it is necessary and sufficient that the sum of the coefficients of the linear combination be equal to two. In this case, these algebras are F 4-algebras. Досліджено алгебри, породжені ідемпотентами, лінійна комбінація яких дорівнює одиниці, на наявність в них поліноміальних тотожностей. Доведено, що у випадку, коли кількість ідемпотентів більша або дорівнює п'яти, такі алгебри не є PI-алгебрами. У випадку чотирьох ідемпотентів для того, щоб алгебра була PI-алгеброю, необхідно і достатньо, щоб сума коефіцієнтів лінійної комбінації дорівнювала двом; у цьому випадку такі алгебри є F 4-алгебрами. Institute of Mathematics, NAS of Ukraine 2004-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3798 Ukrains’kyi Matematychnyi Zhurnal; Vol. 56 No. 6 (2004); 782–795 Український математичний журнал; Том 56 № 6 (2004); 782–795 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/3798/4316 https://umj.imath.kiev.ua/index.php/umj/article/view/3798/4317 Copyright (c) 2004 Rabanovych V. I.; Samoilenko Yu. S.; Strilets O. V. |
| spellingShingle | Rabanovych, V. I. Samoilenko, Yu. S. Strilets, O. V. Рабанович, В. И. Самойленко, Ю. С. Стрелец, А. В. Рабанович, В. И. Самойленко, Ю. С. Стрелец, А. В. On the identities in algebras generated by linearly connected idempotents |
| title | On the identities in algebras generated by linearly connected idempotents |
| title_alt | О тождествах в алгебрах, порожденных линейно связанными идемпотептами |
| title_full | On the identities in algebras generated by linearly connected idempotents |
| title_fullStr | On the identities in algebras generated by linearly connected idempotents |
| title_full_unstemmed | On the identities in algebras generated by linearly connected idempotents |
| title_short | On the identities in algebras generated by linearly connected idempotents |
| title_sort | on the identities in algebras generated by linearly connected idempotents |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3798 |
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