Geodesic
Enumeration of bi-commutative--AG-groupoids
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 3, pp. 314-330.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we introduce (left, right) bi-commutative AG-groupoids and provide a simple method to test whether an arbitrary AG-groupoid is bi-commutative AG-groupoid or not. We also explore some of the general properties of these AG-groupoids. Further we introduce and study some properties of ideals in these AG-groupoids and decompose left commutative AG-groupoids by defining some congruences on these AG-groupoids.
Keywords: (left, right) commutative AG-groupoids.
Mots-clés : AG-groupoid, Bi-Commutative–AG-groupoids 
@article{JSFU_2020_13_3_a5,
     author = {Muhammad Rashad and Imtiaz Ahmad and Muhammad Shah and A. Borumand Saeid},
     title = {Enumeration of {bi-commutative--AG-groupoids}},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {314--330},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2020_13_3_a5/}
}
TY  - JOUR
AU  - Muhammad Rashad
AU  - Imtiaz Ahmad
AU  - Muhammad Shah
AU  - A. Borumand Saeid
TI  - Enumeration of bi-commutative--AG-groupoids
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2020
SP  - 314
EP  - 330
VL  - 13
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2020_13_3_a5/
LA  - en
ID  - JSFU_2020_13_3_a5
ER  - 
%0 Journal Article
%A Muhammad Rashad
%A Imtiaz Ahmad
%A Muhammad Shah
%A A. Borumand Saeid
%T Enumeration of bi-commutative--AG-groupoids
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2020
%P 314-330
%V 13
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2020_13_3_a5/
%G en
%F JSFU_2020_13_3_a5
Muhammad Rashad; Imtiaz Ahmad; Muhammad Shah; A. Borumand Saeid. Enumeration of bi-commutative--AG-groupoids. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 3, pp. 314-330. http://geodesic.mathdoc.fr/item/JSFU_2020_13_3_a5/

[1] M. Naseeruddin, Some studies on almost semigroups and flocks, PhD thesis, The Aligarh Muslim University, India, 1970 | MR

[2] J.R. Cho, J. Jezek, T. Kepka, “Paramedial Groupoids”, Czechoslovak Mathematical Journal, 49:124 (1996), 277–290 | DOI | MR

[3] M. Khan, Faisal, V. Amjad, “On some classes of Abel-Grassmann's groupoids”, J. Adv. Res. Pure Math., 3:4 (2011), 109–119 | DOI | MR

[4] M. Rashad, I. Ahmad, M. Shah, Amanullah, “Stein AG-groupoids”, Sindh University Research Journal (Science Series), 48:3 (2016), 679–684 | MR

[5] M. Shah, I. Ahmad, A. Ali, “Discovery of new classes of AG-groupoids”, Research Journal of Recent Sciences, 1:11 (2012), 47–49

[6] M. Shah, I. Ahmad, A. Ali, “On introduction of new classes of AG-groupoids”, Research Journal of Recent Sciences, 2:1 (2013), 67–70

[7] M. Iqbal, I. Ahmad, “Ideals in CA-AG-groupoids”, Indian J. Pure Appl. Math., 49:2 (2018), 265–284 | DOI | MR

[8] I. Ahmad, Iftikhar Ahmad, M. Rashad, “A study of anti-commutativity in AG-groupoids”, Punjab Univ. J. Math., 48:1 (2016), 99–109 | MR | Zbl

[9] M. Rashad, I. Ahmad, Amanullah, M. Shah, “A study on Cheban Abel-Grassmann's groupoids”, Punjab Univ. J. Math., 51:2 (2019), 79–90 | MR

[10] I. Ahmad, M. Rashad, M. Shah, “Some Properties of AG*-groupoid”, Research Journal of Recent Sciences, 2:4 (2013), 91–93

[11] I. Ahmad, M. Rashad, M. Shah, “Some new result on T$^{1}$, T$^{2}$ and T$^{4}$-AG-groupoids”, Research Journal of Recent Sciences, 2:3 (2013), 64–66

[12] M. Rashad, I. Ahmad, Amanullah, M. Shah, “On relations between right alternative and nuclear square AG-groupoids”, Int. Math. Forum, 8:5–8 (2013), 237–243 | DOI | MR | Zbl

[13] M. Rashad, I. Ahmad, M. Shah, “Left transitive AG-groupoids”, Sindh University Research Journal (Science Series), 46:4 (2014), 547–552

[14] M. Iqbal, I. Ahmad, “Some Congruences on CA-AG-groupoids”, Punjab University. J. Math., 51:3 (2019), 71–87 | MR

[15] M. Rashad, I. Ahmad, “A note on unar LA-semigroup”, Punjab Univ. J. Math., 50:3 (2018), 113–121 | MR

[16] Muhammad Shah, A theoretical and computational investigation of AG-groups, PhD thesis, Quaid-i-Azam University, Islamabad, 2012

[17] N. Bobeica, Liubomir Chiriac, “On toplogical AG-groupoids and paramedial quasigroups with multiple identities”, ROMAI Journal, 6:1 (2010), 5–14 | MR | Zbl

[18] Amanullah, M. Rashad, I. Ahmad, “Abel Grassmann's Groupoids of Modulo Matrices”, Mehran University research Journal of Engineering and Technology, 35:1 (2016), 63–70 | MR

[19] Amanullah, M. Rashad, I. Ahmad, M. Shah, “On Modulo AG-groupoids”, Journal of Advances in Mathematics, 8:3 (2014), 1606–1613

[20] T. Shah, Inayat Ur Rahman, “On LA-rings of finitely nonzero function”, Int. J. Contemp. Math. Sciences, 5:5 (2010), 209–222 | MR | Zbl

[21] T. Shah, M. Raees, Gohar Ali, “On LA-Modules”, Int. J. Contemp. Math. Sciences, 6:21 (2011), 999–1006 | MR | Zbl

[22] Q. Mushtaq, M. Khan, “Ideals in AG-band and AG$^{\ast}$-groupoids”, Quasigroups and Related system, 14 (2006), 207–215 | MR | Zbl

[23] P.V. Protic, “Congruences on an inverse AG$^{\ast\ast}$-groupoid via the natural partial order”, Quasigroups and related system, 17:2 (2009), 283–290 | MR | Zbl

[24] P.V. Protic, N. Stevanovic, “AG-test and some general properties of AG-groupoids”, Pure Mathematics and Applications, 6:4 (1995), 371–383 | MR | Zbl

[25] T. Shah, Inayat Ur Rahman, “On $\Gamma$-ideals and $\Gamma$-bi-ideals in $\Gamma$-AG-groupoids”, International journal of Algebra, 4:6 (2010), 267–276 | MR | Zbl

[26] A. Khan, M. Shabir, Young Bae Jun, “Generalized fuzzy Abel Grassmann's Groupoids”, International Journal of Fuzzy Systems, 12:4 (2010), 340–349 | MR

[27] Asghar Khan, Young Bae Jun, Tahir Mahmmod, “Generalized fuzzy interior ideals in Abel Grassmann's Groupoids”, International journal of Mathematics and Mathematical Sciences, 2010, 838392 | DOI | MR | Zbl

[28] V. Celakoska-Jordanova, Biljiana Janeva, Free left commutative Groupoids

[29] GAP: Groups Algorithm and Programming, Version 4.4.12, 2008

[30] B.D. McKay, I.M. Wanless, “On the number of Latin squares”, Ann. Combin., 9 (2005), 335–344 | DOI | MR | Zbl

[31] J. Slaney, FINDER, Notes and Guide, Center of Information Science and Research, Australian National University, 1995

[32] A. Ali, J. Slaney, “Counting loops with the inverse property image”, Quasigroups and Related System, 16:1 (2008), 13–16 | MR | Zbl

[33] A. Distler, T. Kelsey, “The monoids of order eight and nine”, Proc. of AISC 2008, LNCS, 5144, Springer, 2008, 61–76 | MR | Zbl

[34] A. Distler, T. Kelsey, “The monoids of order eight and nine and ten”, Ann. Math. Artif. Intell., 56:1 (2009), 3–21 | DOI | MR | Zbl

[35] A. Distler, Classification and Enumeration of Finite semigroups, PhD thesis, University of St. Andrews, 2010 | Zbl

[36] A. Distler, M. Shah, V. Sorge, “Enumeration of AG-groupoids”, CICM 2011, Lecture Notes in Computer Science, 6824, 2011, 1–14 | DOI | Zbl

[37] Q. Mushtaq, M. Khan, “Decomposition of AG$^{\ast}$-groupoids”, Quasigroups and related system, 15 (2007), 303–308 | MR | Zbl

[38] W.A. Dudek, R.S. Gigon, “Congruences on completely inverse AG$^{\ast\ast}$-groupoids”, Quasigroups and Related System, 20 (2012), 203–209 | MR | Zbl