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Counting of Conjugacy classes in partial transformation semigroup. | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 157، دوره 13، شماره 1، خرداد 2022، صفحه 1909-1915 اصل مقاله (135.98 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.24082.2666 | ||
| نویسندگان | ||
| Aftab Hussain Shah؛ Mohd Rafiq Parray؛ Dilawar Juneed Mir* | ||
| Department of Mathematics, Central University of Kashmir, Ganderbal-191201, India | ||
| تاریخ دریافت: 05 مرداد 1400، تاریخ پذیرش: 22 آبان 1400 | ||
| چکیده | ||
| J.Koneiczny in [8] introduced the new notion $\sim_{n}$ notion of conjugacy in semigroups. In this paper, we count the number of conjugacy classes in Partial Transformation semigroup $\mathcal{P}(A)$ for an infinite set $A$ with respect to $\sim_{n}$ notion of conjugacy. | ||
| کلیدواژهها | ||
| Conjugacy؛ Diagraph؛ Double Ray؛ Cycle set؛ Chain | ||
| مراجع | ||
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[1] A. H. Shah and M. R. Parray, On ∼n notion of conjugacy in semigroups, to appear. [2] D. J. Mir, A. H. Shah and S. A. Ahanger, On automorphisms of monotone transformation posemigroups, AsianEur. J. Math., https://doi.org/10.1142/S1793557122500322 (2021). [3] F. Otto, Conjugacy in monoids with a special Church-Rosser presentation is decidable, Semigroup Forum, 29 (1984) 223-240. [4] G. Kudryavtseva and V. Mazorchuk, On three approaches to conjugacy in semigroups, Semigroup Forum, 78 (2009) 14-20. [5] G. Lallement, Semigroups and Combinatorial Applications, John Wiley and Sons, New York, 1979. [6] J. Araujo, M. Kinyon, J. Konieczny and A. Malheiro, Four notions of conjugacy for abstract semigroups, to appear in Proc. Roy. Soc. Edinburgh Sect. A, preprint (2015), arXiv:1503.00915v2. [7] J. Araujo, J. Konieczny and A. Malheiro, Conjugation in semigroups, J. Algebra, 403 (2014) 93-134. [8] J. Koneicny, A new definition of conjugacy for semigroups, J. Algebra and Appl., 17(02)(2018) 185002. [9] J. M. Howie, Fundamentals of Semigroup Theory, Oxford University Press, New York, 1995. [10] T. Jech, Set Theory, Third Edition, Springer-Verlag, New York, 2006. | ||
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