New results over Zappa-Szép products via a recent semigroup

Year 2024, Volume: 53 Issue: 5, 1238 - 1249, 15.10.2024

Nurten Urlu Özalan

https://doi.org/10.15672/hujms.1085952

Abstract

In [16], the authors established a new semigroup ${\mathcal N}$ as an extension of both the Rees matrix and completely zero-simple semigroups. In this paper, by taking into account the Zappa-Szép product obtained by special subsemigroups of ${\mathcal N}$, we will expose some new distinguishing theoretical results on this product.

Keywords

Zappa-Szép products, Rees matrix semigroup, completely 0-simple semigroup, Green relations

References

• [1] F. Ates and A.S. Cevik, Knit products of finite cyclic groups and their applications, Rend. Semin. Mat. Univ. Padova, 121, 1-12, 2009.
• [2] M.G. Brin, On the Zappa-Szép product, Comm. Algebra, 33, 393-424, 2005.
• [3] A.S. Cevik, S.A.Wazzan and F. Ates, A higher version of Zappa products for monoids, Hacet. J. Math. Stat. 50 (1), 224-235, 2021.
• [4] N.D. Gilbert and S. Wazzan, Zappa-Szép products of bands and groups, Semigroup Forum, 77, Article number: 438, 2008.
• [5] V. Gould and R.-E. Zenab, Restriction semigroups and λ-Zappa-Szép products, Period. Math. Hungar. 73, 179-207, 2016.
• [6] M. Kunze, Zappa products, Acta Math. Hungar. 41, 225-239, 1983.
• [7] T.G. Lavers, Presentations of general products of monoids, J. Algebra, 204, 733-741, 1998.
• [8] M.V. Lawson, A correspondence between a class of monoids and self-similar group actions I, Semigroup Forum, 76, 489-517, 2008.
• [9] M.V. Lawson and A.R. Wallis, A correspondence between a class of monoids and self-similar group actions II, Inter. J. Algeb. Comput. 25 (4), 633-668, 2015.
• [10] B.L. Madison, T.K. Mukherjee and M.K. Sen, Periodic properties of groupbound semigroups, Semigroup Forum, 22, 225-234, 1981.
• [11] P.W. Michor, Knit products of graded Lie algebras and groups, Rend. Circ. Mat. Palermo (2) Suppl. 2 (22), 171-175, 1989.
• [12] Š. Schwarz, The theory of characters of finite commutative semigroups, Czechoslovak Math. J. 4 (79), 219-247, 1954.
• [13] Š. Schwarz, The theory of characters of commutative Hasdorff bicompact semigroups, Czechoslovak Math. J. 6 (81), 330-361, 1956.
• [14] J.T. Sedlock, Green’s relations on a periodic semigroup, Czechoslovak Math. J., 19 (2), 318-323, 1969.
• [15] J. Szép, On the structure of groups which can be represented as the product of two subgroups, Acta Sci. Math. Szeged, 12, 57-61, 1950.
• [16] N.U. Ozalan, A.S. Cevik, E.G. Karpuz, A new semigroup obtained via known ones, Asian-Eur. J. Math. 12 (6), 2040008, 2019.
• [17] S. Wazzan, Zappa-Szép products of semigroups, Applied Mathematics, 6 (6), 1047- 1068, 2015.
• [18] S.A. Wazzan, F. Ates and A.S. Cevik, The New Derivation for Wreath Products of Monoids, Filomat, 34 (2), 683-689, 2020.
• [19] S.A. Wazzan and N. U. Ozalan On classification of semigroup by Greens Theorem, J. Math. Article ID 9193446, 7 pages, 2022.
• [20] G. Zappa, Sulla construzione dei gruppi prodotto di due sottogruppi permutabili tra loro, Atti Secondo Congresso Un. Ital., Bologna 1940. Edizioni Rome: Cremonense, 119-125, 1942.