TY - JOUR T1 - New results over Zappa-Szép products via a recent semigroup AU - Urlu Özalan, Nurten PY - 2024 DA - October DO - 10.15672/hujms.1085952 JF - Hacettepe Journal of Mathematics and Statistics PB - Hacettepe University WT - DergiPark SN - 2651-477X SP - 1238 EP - 1249 VL - 53 IS - 5 LA - en AB - 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. KW - Zappa-Szép products KW - Rees matrix semigroup KW - completely 0-simple semigroup KW - Green relations CR - [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. CR - [2] M.G. Brin, On the Zappa-Szép product, Comm. Algebra, 33, 393-424, 2005. CR - [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. CR - [4] N.D. Gilbert and S. Wazzan, Zappa-Szép products of bands and groups, Semigroup Forum, 77, Article number: 438, 2008. CR - [5] V. Gould and R.-E. Zenab, Restriction semigroups and λ-Zappa-Szép products, Period. Math. Hungar. 73, 179-207, 2016. CR - [6] M. Kunze, Zappa products, Acta Math. Hungar. 41, 225-239, 1983. CR - [7] T.G. Lavers, Presentations of general products of monoids, J. Algebra, 204, 733-741, 1998. CR - [8] M.V. Lawson, A correspondence between a class of monoids and self-similar group actions I, Semigroup Forum, 76, 489-517, 2008. CR - [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. CR - [10] B.L. Madison, T.K. Mukherjee and M.K. Sen, Periodic properties of groupbound semigroups, Semigroup Forum, 22, 225-234, 1981. CR - [11] P.W. Michor, Knit products of graded Lie algebras and groups, Rend. Circ. Mat. Palermo (2) Suppl. 2 (22), 171-175, 1989. CR - [12] Š. Schwarz, The theory of characters of finite commutative semigroups, Czechoslovak Math. J. 4 (79), 219-247, 1954. CR - [13] Š. Schwarz, The theory of characters of commutative Hasdorff bicompact semigroups, Czechoslovak Math. J. 6 (81), 330-361, 1956. CR - [14] J.T. Sedlock, Green’s relations on a periodic semigroup, Czechoslovak Math. J., 19 (2), 318-323, 1969. CR - [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. CR - [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. CR - [17] S. Wazzan, Zappa-Szép products of semigroups, Applied Mathematics, 6 (6), 1047- 1068, 2015. CR - [18] S.A. Wazzan, F. Ates and A.S. Cevik, The New Derivation for Wreath Products of Monoids, Filomat, 34 (2), 683-689, 2020. CR - [19] S.A. Wazzan and N. U. Ozalan On classification of semigroup by Greens Theorem, J. Math. Article ID 9193446, 7 pages, 2022. CR - [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. UR - https://doi.org/10.15672/hujms.1085952 L1 - https://dergipark.org.tr/en/download/article-file/2302401 ER -