Direct products of cyclic semigroups and left zero semigroups in $\beta\mathbb{N}$ | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 10، دوره 20، شماره 1، فروردین 2024، صفحه 221-232 اصل مقاله (507.6 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.48308/cgasa.2023.233625.1436 | ||
| نویسنده | ||
| Yuliya Zelenyuk* | ||
| School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa. | ||
| چکیده | ||
| We show that for every $n\in\mathbb{N}$, the direct product of the cyclic semigroup of order $n$ and period $1$ and the left zero semigroup $2^\mathfrak{c}$ has copies in $\beta\mathbb{N}$. | ||
| کلیدواژهها | ||
| Stone-\v{C}ech compactification؛ idempotent؛ right cancelable ultrafilter؛ cyclic semigroup؛ left zero semigroup | ||
| مراجع | ||
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[1] Bergelson, V. and Hindman, N., Some new multi-cell Ramsey theoretic results, Proc. Amer. Math. Soc., Ser. B 8 (2021), 358-370. [2] Davenport, D., Hindman, N., Leader, I., and Strauss, D., Continuous homomorphisms on βN and Ramsey theory, New York J. Math. 6 (2000), 73-86. [3] Douwen, E.V., The ˇ Cech-Stone compactification of a discrete groupoid, Topology Appl. 39 (1991), 43-60. [4] Hindman, N. and Strauss, D., “Algebra in the Stone-ˇCech Compactification”, De Gruyter, 1998. [5] Hindman, N., Strauss, D., and Zelenyuk, Y., Large rectangular semigroups in Stone-ˇ Cech compactifications, Trans. Amer. Math. Soc. 355 (2003), 2795-2812. [6] Strauss, D., N∗ does not contain an algebraic and topological copy of βN, J. London Math. Soc. 46 (1992), 463-470. [7] Zelenyuk, Y., Elements of order 2 in βN, 252 (2021), 355-360. [8] Zelenyuk, Y., Finite semigroups in βN and Ramsey theory, Bull. London Math. Soc. 53 (2021), 710-722. [9] Zelenyuk, Y., Elements of finite order in βN, Adv. Math. 408 (2022), 108608. [10] Zelenyuk, Y. and Zelenyuk, Yu., Direct products of null semigroups and rectangul arbands in βN, New York J. Math. 28 (2022), 610-616. | ||
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