Left and Right Transposition Regular $\Gamma$-TA-Groupoids
Keywords:
$\Gamma$-TA-groupoid, Left transposition regular $\Gamma$-TA-groupoid, Right transposition regular $\Gamma$-TA-groupoid, Groupoid, $\Gamma$-GroupoidAbstract
This paper introduces an innovative algebraic concept called the transposition regular -TA-groupoid. The study focuses on investigating the fundamental properties and structural characteristics of the regular associative
-TA-groupoid. The results demonstrate that every left transposition regular
-TA-groupoid is always a
-semigroup. Furthermore, it is proved that every left transposition regular
-TA-groupoid is also a right transposition regular
-TA-groupoid, and conversely, every right transposition regular
-TA-groupoid is a left transposition regular
-TA-groupoid. These findings reveal a relationship between the two forms of
-TA-groupoids and provide deeper insight into the structural behavior of
-TA-groupoids within the framework of algebraic regularity.
References
Ahmad, I., Rashad, M., & Shah, M. (2013). Some properties of AG*-groupoid. Research Journal of Recent Sciences, 2(4), 91-93.
An, X.G., Chen, M.M., & Zhang, X.H. (2022a). An open problem on Tarski associative NET-groupoids and GTA-NET-groupoids. International Journal of Pure and Applied Mathematics, 47, 1091-1112.
An, X., & Zhang, X. (2022). Transposition regular TA-groupoids and their structures. Axioms, 11(8), 378. https://doi.org/10.3390/axioms11080378
An, X., Zhang, X., & Ma, Z. (2022). Two open problems on CA-groupoids and cancellativities of T2CA-groupoids. Axioms, 11(4), 169. https://doi.org/10.3390/axioms11040169
Bhargavi, Y., Eswarlal, T., & Ragamayi, S. (2020). Cartesian product on fuzzy ideals of a ternary -semigroup. Advances in Mathematics: Scientific Journal, 9(3), 1197-1203. https://doi.org/10.37418/amsj.9.3.44
Chattopadhyay, S. (2010). A semihypergroup associated with a -semigroup. Analele Stiintifice Ale Universitatii “Ali Cuza” Din Iasi (SN) Mathematica, f1, 209-225.
Chen, M., Du, Y., & An, X. (2023). Research on a class of special quasi TA-neutrosophic extended triplet: TA-groups. Neutrosophic Sets and Systems, 57, 408-422.
Chuphan, S., & Yiarayong, P. (2023). Theory of paramedial -right almost semigroups. Rattanakosin Journal of Science and Technology, 5(1), 20-27.
Du, Y., Zhang, X., & An, X. (2022). Transposition regular AG-groupoids and their decomposition theorems. Mathematics, 10, 1396. https://doi.org/10.3390/math10091396
Faisal, Y., Yaqoob, N., & Hila, K. (2012). On fuzzy (2, 2) -regular ordered-AG**-groupoids. U.P.B. Sci. Bull., Series A, 74(2), 87-104.
Jantanan, W., Nuadthaisong, K., & Jaroenram, S. (2021). On ordered -semigroups containing two-sided bases. BURAPHA SCIENCE JOURNAL, 26(3), 1409-1419.
Kehayopulu, N. (2009). On le- -semigroups. In International Mathematical Forum, 4(39), 1915-1922.
Ma, Z., Zhang, X., & Smarandache, F. (2020). Some results on various cancellative CA-groupoids and variant CA-groupoids. Symmetry, 12(2), 315. https://doi.org/10.3390/sym12020315
Mushtaq, Q., & Khan, M. (2006). Ideals in AG-band and AG-groupoid. Quasigroups and Related Systems, 16(2), 207-215.
Rashad, M., Ahmad, I., Shah, M., & Khuhro, Z. U. A. (2014). Left transitive AG-groupoids. Sindh Univ. Res. Jour. (Sci. Ser.), 46(4), 547-552.
Sabri, S. (2013). Idempotent -semigroups. Scientific researches of the Union of Scientists in Bulgaria-Plovdiv, series B. Natural Sciences and the Humanities, 15, 101-106.
Sen, M.K., & Saha, N.K. (1986). On -semigroup I, Bulletin of the Calcutta Mathematical Society. 78, 180-186.
Shah, T., & Rehman, I. (2010). On -ideals and -bi-ideals in -AG-groupoids. International journal of Algebra, 4(6), 267-276.
Shah, T., & Rehman, I. (2013). Decomposition of locally associative -AG-groupoids. Novi Sad Journal of Mathematics, 43(1), 1-8.
Singh, Y. S., & Khan, M. R. (2010). Regular quasi- -absorbent in -groupoid-lattices. International Journal of Open Problems in Computer Science and Mathematics, 3(5), 190-200.
Smisha, M. A., & Romeo, P. G. (2021). On the embedding of - semigroup Amalgam using partial -groupoid. Advances in Algebra (AA), 14(1), 3-13.
Yiarayong, P. (2022). Non-associative algebras, 1st ed., THAMMASAT UNIVERSITY PRESS.
Zhang, X., & Du, Y. (2022). Left (right) regular and transposition regular semigroups and their structures. Mathematics, 10, 1021. https://doi.org/10.3390/math10071021
Zhang, X., Yuan, W., & Chen, M. (2020a). A kind of non-associative groupoids and quasi neutrosophic extended triplet groupoids (QNET-groupoids). Neutrosophic Sets Syst, 36, 144-163.
Zhang, X., Yuan, W., Chen, M., & Smarandache, F. (2020b). A kind of variation symmetry: Tarski associative groupoids (TA-groupoids) and Tarski associative neutrosophic extended triplet groupoids (TA-NET-groupoids). Symmetry, 12, 714. https://doi.org/10.3390/sym12050714
Downloads
Published
Issue
Section
Categories
License
Copyright (c) 2026 Journal of Applied Science and Emerging Technology
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
