Regularity of the partial Baer-Levi semigroups with restricted range
Let \(Y\) be a fixed nonempty subset of an infinite set \(X\) and let \(q\) be an infinite cardinal such that \(q\leq|X|\). Let \(PS(X,Y,q)\) denote the semigroup of all partial injective transformations from \(X\) into \(Y\) for which the complement of its range has cardinality \(q\). Then \(PS(X,Y...
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| Дата: | 2026 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2026
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2440 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Репозитарії
Algebra and Discrete Mathematics| Резюме: | Let \(Y\) be a fixed nonempty subset of an infinite set \(X\) and let \(q\) be an infinite cardinal such that \(q\leq|X|\). Let \(PS(X,Y,q)\) denote the semigroup of all partial injective transformations from \(X\) into \(Y\) for which the complement of its range has cardinality \(q\). Then \(PS(X,Y,q)\) is a generalization of the partial Baer-Levi semigroup. In this paper, we study several types of regularity on \(PS(X, Y,q)\). We characterize all regular, left regular, right regular, completely regular, intra-regular and coregular elements and determine the largest regular subsemigroup of this semigroup. Furthermore, when \(Y\) is finite, we present formulas for counting the total number of elements of each type mentioned above. |
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| DOI: | 10.12958/adm2440 |