TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Freq.: MONTHLY - Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

On LA-Gamma-semihypergroups containing two-sided bases

, , , , , *

* Corresponding author · click or hover a name for details

pp. 441–456Vol. 27Issue 3April 2024DOI: 10.47974/JIM-1521XML
Received:
08 Dec 2021
Published Online:
07 May 2024
Article type:
Research Article
Language:
EN
Article no.:
JIM-1521
Pages:
441–456

Abstract

Ideal theory and base theory of algebraic structures play an important role in studied. In this study, we focus on studying bases of ideals in algebraic structures. The algebraic structure LA-Γ-semihypergroups is very interesting to study. This structure is generalization of many algebraic structures, for example, commutative semigroups, commutative Γ-semigroups, LA-semigroups, LA-Γ-semigroups, commutative semihypergroups, etc. Many results in these algebraic structures were extended to results in LA-Γ-semihypergroups. On the other hand, the results in these structures are the special cases of results in LA-Γ-semihypergroups. The main purpose of this paper is to introduce the notion of two-sided base of an LA-Γ-semihypergroup with pure left identity. We prove that every two-sided base of an LA-Γ-semihypergroup with pure left identity is one-element base. Finally, we prove that the compliment of union of all two-sided base of an LA-Γ-semihypergroup with pure left identity is maximal proper Γ-hyperideal.

Keywords

Subject Classifications

16Y6008A7203G2503E72

References

[1] M. Aslam, T. Aroob and N. Yaqoob, On cubic Γ-hyperideals in left almost Γ-semihypergronps, Annals of Fizzy Mathcmatics and informatics. vol. 5, no. 1, pp. 169-182, 2013.
[2] T. Changphas, P. Kummon, On Γ-semigroups containing two-sided bases, KKU Science Journal. vol. 46, no. 1, pp. 154-161, 2018.
[3] I. Fabrici, Two-sided bases of semigroups, Matematicky casopis, vol. 25, no. 2, pp. 173-178, 1975.
[4] F. Marty, Sur une generalization de la notion de groupe, 8th congres Math. Scandinaves, Stockholm, pp. 45-49, 1934.
[5] M.K. Sen, On Γ-semigroups, Proceeding of International Symposium on Algebra and Its Applications. Decker Publication. New York. vol. 91, no. 1, pp. 301-308, 1981.
[6] N. Yaqoob, Applications of rough sets to Γ-hyperideals in left almost Γ-semihypergroups, Neural Computing and Applications, vol. 21, no. 1, pp. 267-273, 2012.
[7] N. Yaqoob, M. Aslam, On bi-Γ-hyperideals in left almost 
Γ-semihypergroups, J. Adv. Res. Pure Math., vol. 4, no. 1, pp. 130-143, 2012.
[8] N. Yagoob, M. Aslam, M.A. Ansari, Structures of N-Γ-hyperideals in left almost Γ semihypergroups, World Applied Sciences Journal. vol. 17, no. 12, 1611-1617, 2012.
[9] N. Yaqoob, M. Aslam, Faisal, On soft Γ-hyperideals over left almost Γ-semihypergroups, Journal of Advanced Research in Dynamical and Control Systems, vol. 4, no. 1, pp. 1-12, 2012.

Views: 213Downloads: 5Citations: 0