Free products of $n$-tuple semigroups
We construct a free product of arbitrary n-tuple semigroups, introduce the notion of $n$-band of $n$-tuple semigroups and, in terms of this notion, describe the structure of the free product. We also construct a free commutative $n$-tuple semigroup of an arbitrary rank and characterize one-generated...
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| Дата: | 2018 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2018
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/1652 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We construct a free product of arbitrary n-tuple semigroups, introduce the notion of $n$-band of $n$-tuple semigroups and, in terms of this notion, describe the structure of the free product. We also construct a free commutative $n$-tuple semigroup of an arbitrary rank and characterize one-generated free commutative $n$-tuple semigroups. Moreover, we describe the least commutative congruence on a free $n$-tuple semigroup and establish that the semigroups of the constructed free commutative $n$-tuple semigroup are isomorphic and its automorphism group is isomorphic to the symmetric group. |
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