Characterizations of intra-regular <i>LA</i>-semihyperrings in terms of their hyperideals

Warud Nakkhasen; Warud Nakkhasen

doi:10.3934/math.2022324

AIMS Mathematics

2022, Volume 7, Issue 4: 5844-5859. doi: 10.3934/math.2022324

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Characterizations of intra-regular LA-semihyperrings in terms of their hyperideals

Warud Nakkhasen ^,

Department of Mathematics, Faculty of Science, Mahasarakham University, Maha Sarakham 44150, Thailand

Received: 01 October 2021 Revised: 05 December 2021 Accepted: 04 January 2022 Published: 12 January 2022
MSC : 16Y60, 20M17, 20N20

The purpose of this article is to investigate the class of intra-regular $ LA $-semihyperrings. Then, characterizations of intra-regular $ LA $-semihyperrings by the properties of many types of their hyperideals are obtained. Moreover, we present a construction of $ LA $-semihyperrings from ordered $ LA $-semirings.
- $ LA $-semihypergroup,
- $ LA $-semihyperring,
- intra-regular $ LA $-semihyperring
Citation: Warud Nakkhasen. Characterizations of intra-regular LA-semihyperrings in terms of their hyperideals[J]. AIMS Mathematics, 2022, 7(4): 5844-5859. doi: 10.3934/math.2022324

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Abstract

The purpose of this article is to investigate the class of intra-regular $ LA $-semihyperrings. Then, characterizations of intra-regular $ LA $-semihyperrings by the properties of many types of their hyperideals are obtained. Moreover, we present a construction of $ LA $-semihyperrings from ordered $ LA $-semirings.

References

[1]	A. Alsubie, A. Al-Masarwah, MBJ-neutrosophic hyper $BCK$-ideals in hyper $BCK$-algebras, AIMS Math., 6 (2021), 6107–6121. http://dx.doi.org/10.3934/math.2021358 doi: 10.3934/math.2021358
[2]	I. Ahmad, S. Rahman, M. Iqbal, Amanullah, A note on left abelian distributive $LA$-semigroups, Punjap Univ. J. Math., 52 (2020), 47–63.
[3]	S. Abdullah, S. Aslam, N. U. Amin, $LA$-semigroups characterized by the properties of interval valued $(\alpha, \beta)$-fuzzy ideals, J. Appl. Math. Inform., 32 (2014), 405–426. https://doi.org/10.14317/JAMI.2014.405 doi: 10.14317/JAMI.2014.405
[4]	M. A. Ansari, Roughness in generalized $(m, n)$ bi-ideals in ordered $LA$-semigroups, Int. J. Math. Comput. Sc., 14 (2019), 371–386.
[5]	M. Azhar, M. Gulistan, N. Yaqoob, S. Kadry, On fuzzy ordered $LA$-semihypergroups, Int. J. Anal. Appl., 16 (2018), 276–289. https://doi.org/10.28924/2291-8639-16-2018-276 doi: 10.28924/2291-8639-16-2018-276
[6]	V. Amjad, F. Yousafzai, On pure $LA$-semihypergroups, Konuralp J. Math., 2 (2014), 53–63.
[7]	N. Abughazalah, N. Yaqoob, A. Bashir, Cayley graphs over $LA$-groups and $LA$-polygroups, Math. Probl. Eng., 2021 (2021), 4226232, 9 pages. https://doi.org/10.1155/2021/4226232 doi: 10.1155/2021/4226232
[8]	A. Basar, A note on $(m, n)$-$\Gamma$-ideals of ordered $LA$-$\Gamma$-semigroups, Konuralp J. Math., 7 (2019), 107–111.
[9]	S. I. Batool, I. Younas, M. Khan, N. Yaqoob, A new technique for the construction of confusion component based on inverse $LA$-semigroups and its application in stenography, Multimed. Tools Appl., 80 (2021), 28857–28877. https://doi.org/10.1007/s11042-021-11090-w doi: 10.1007/s11042-021-11090-w
[10]	P. Corsini, Prolegomena of hypergroup theory, Aviani Editore, 1993.
[11]	P. Corsini, V. Leoreanu, Applications of hyperstructure theory, Springer Science & Business Media, 2003.
[12]	B. Davvaz, S. Subiono, M. A. Tahan, Calculus of meet plus hyperalgebra (tropical semihyperrings), Commun. Algebra, 48 (2020), 2143–2159. https://doi.org/10.1080/00927872.2019.1710178 doi: 10.1080/00927872.2019.1710178
[13]	A. Elmoasy, On rough fuzzy prime ideals in left almost semigroups, Int. J. Anal. Appl., 19 (2021), 455–464.
[14]	M. Gulistan, M. Khan, N. Yaqoob, M. Shahzad, Structural properties of cubic sets in regular $LA$-semihypergroups, Fuzzy Inform. Eng., 9 (2017), 93–116. https://doi.org/10.1016/j.fiae.2017.03.005 doi: 10.1016/j.fiae.2017.03.005
[15]	M. Gulistan, N. Yaqoob, S. Kadry, M. Azhar, On generalized fuzzy sets in ordered $LA$-semihypergroups, P. Est. Acad. Sci., 68 (2019), 43–54. https://doi.org/10.3176/proc.2019.1.06 doi: 10.3176/proc.2019.1.06
[16]	K. Hila, J. Dine, On hyperideals in left almost semihypergroups, International Scholarly Research Notices, 2011 (2011), 953124. https://doi.org/10.5402/2011/953124 doi: 10.5402/2011/953124
[17]	M. Hu, F. Smarandache, X. Zhang, On neutrosophic extended triplet $LA$-hypergroups and strong pure $LA$-semihypergroups, Symmetry, 12 (2020), 163. https://doi.org/10.3390/sym12010163 doi: 10.3390/sym12010163
[18]	W. Jantanan, R. Chinram, P. Petchkaew, On $(m, n)$-quasi-gamma-ideals in ordered $LA$-gamma-semigroups, J. Math. Comput. Sci., 11 (2021), 3377–3390. https://doi.org/10.28919/jmcs/5705 doi: 10.28919/jmcs/5705
[19]	A. Khan, M. Farooq, M. Izhar, B. Davvaz, Fuzzy hyperideals of left almost semihypergroups, Int. J. Anal. Appl., 15 (2017), 155–171.
[20]	M. A. Kazim, M. Neseeruddin, On almost semigroups, Rort. Math., 36 (1977), 41–47.
[21]	M. Khan, T. Asif, Characterizations of intra-regular left almost semigroups by their fuzzy ideals, J. Math. Res., 2 (2010), 87–96.
[22]	M. Khan, Y. B. Jun, F. Yousafzai, Fuzzy ideals in right regular $LA$-semigroups, Hacet. J. Math. Stat., 44 (2015), 569–586.
[23]	N. Kausar, M. Munir, B. Islam, M. Alesemi, Salahuddin, M. Gulzar, Ideals in $LA$-rings, Ital. J. Pure Appl. Math., 44 (2020), 731–744.
[24]	W. A. Khan, A. Taouti, A. Salami, Z. Hussain, On gamma $LA$-rings and gamma $LA$-semirings, Eur. J. Pure Appl. Math., 14 (2021), 989–1001. https://doi.org/10.29020/nybg.ejpam.v14i3.4034 doi: 10.29020/nybg.ejpam.v14i3.4034
[25]	W. Khan, F. Yousafzai, M. Khan, On generalized ideals of left almost semigroups, Eur. J. Pure Appl. Math., 9 (2016), 277–291.
[26]	C. G. Massouros, N. Yaqoob, On theory of left/right almost groups and hypergroups with their relevant enumerations, Mathematics, 9 (2021), 1828. https://doi.org/10.3390/math9151828 doi: 10.3390/math9151828
[27]	D. Mruduladevi, G. Shobhalatha, T. Padma Praveen, Congruences on la-semirings and variant of semigroup, Int. J. Math. Trends Technol., 40 (2016), 180–182.
[28]	F. Marty, Sur une generalization de la notion de group, 8th Congress Mathematics Scandinaves, Stockholm, 1934.
[29]	W. Nakkhasen, Left almost semihyperrings characterized by their hyperideals, AIMS Math., 6 (2021), 13222–13234. https://doi.org/10.3934/math.2021764 doi: 10.3934/math.2021764
[30]	S. Nawaz, M. Gulistan, S. Khan, Weak $LA$-hypergroups; neutrosophy, enumeration and redox reaction, Neutrosophic Sets Sy., 36 (2020), 352–368.
[31]	S. Nawaz, I. Rehman, M. Gulistan, On left almost semihyperrings, Int. J. Anal. Appl., 16 (2018), 528–541. https://doi.org/10.28924/2291-8639-16-2018-528 doi: 10.28924/2291-8639-16-2018-528
[32]	W. Nakkhasen, B. Pibaljommee, Intra-regular semihyperrings, J. Discret. Math. Sci. C., 22 (2019), 1019–1034. https://doi.org/10.1080/09720529.2019.1649818 doi: 10.1080/09720529.2019.1649818
[33]	P. V. Protić, N. Stevanović, AG-test and some general properties of Abel-Grassmann's groupoids, Pure Math. Appl., 4 (1995), 371–383.
[34]	I. Rehman, A. Razzaque, M. I. Faraz, Neutrosophic set approach to study the characteristic behavior of left almost rings, Neutrosophic Sets Sy., 46 (2021), 24–36.
[35]	I. Rehman, N. Yaqoob, S. Nawaz, Hyperideals and hypersystems in $LA$-hyperrings, Songklanakarin J. Sci. Technol., 39 (2017), 651–657. https://doi.org/10.14456/sjst-psu.2017.80 doi: 10.14456/sjst-psu.2017.80
[36]	A. S. Sezer, Certain characterizations of $LA$-semigroups by soft sets, J. Intell. Fuzzy Syst., 27 (2014), 1035–1046. https://doi.org/10.3233/IFS-131064 doi: 10.3233/IFS-131064
[37]	T. Shah, I. Rehman, On $LA$-rings of finitely nonzero functions, Int. J. Contemp. Math. Sciences, 5 (2010), 209–222.
[38]	J. Tang, X. Y. Xie, Z. Gu, A study on weak hyperfilters of ordered semihypergroups, AIMS Math., 6 (2021), 4319–4330. https://doi.org/10.3934/math.2021256 doi: 10.3934/math.2021256
[39]	T. Vougiouklis, Hyperstructures and their representations, Handronic press, 1994.
[40]	F. Yousafzai, A. Iampam, J. Tang, Study on smallest (fuzzy) ideals of $LA$-semigroups, Thai J. Math., 16 (2018), 549–561.
[41]	I. Younas, Q. Mushtaq, A. Rafiq, Presentation of inverse $LA$-semigroups, Maejo Int. J. Sci. Technol., 14 (2020), 242–251.
[42]	N. Yaqoob, Approximations in left almost polygroups, J. Intell. Fuzzy Syst., 36 (2019), 517–526.
[43]	N. Yaqoob, P. Corsini, F. Yousafzai, On intra-regular left almost semihypergroups with pure left identity, J. Math., 2013 (2013), 510790. https://doi.org/10.1155/2013/510790 doi: 10.1155/2013/510790
[44]	N. Yaqoob, I. Cristea, M. Gulistan, S. Nawaz, Left almost polygroups, Ital. J. Pure Appl. Math., 39 (2018), 465–474.
[45]	N. Yaqoob, M. Gulistan, Partially ordered left almost semihypergroups, J. Egyptian Math. Soc., 23 (2015), 231–235. https://doi.org/10.1016/j.joems.2014.05.012 doi: 10.1016/j.joems.2014.05.012
[46]	P. Yiarayong, On generalizations of quasi-prime ideals of an ordered left almost semigroups, Afrika Mathematika, 32 (2021), 969–982. https://doi.org/10.1007/s13370-021-00873-x doi: 10.1007/s13370-021-00873-x

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