Paramedial and Bol* Abel-Grassmann Groupoids

Authors

  • M. Shah Department of Mathematics, Quaid-e-Azam University, Islamabad, Pakistan.
  • I. Ahmad Department of Mathematics, University of Malakand, Chakdara, Pakistan.

Abstract

We introduce a new class of groupoids which we name Bol*-groupoids. This in turn gives another new class of AG-groupoids that we call Bol*-AG-groupoids. We also enlist two new classes of AG-groupoids namely paramedial AG-groupoids and AG-groupoid-semigroups. The latter is also an interesting new class of semigroups. We discuss some basic properties of these newly introduced classes and provide various finite examples to show their existence.

References

M. Naseeruddin, “Some studies on almost semigroups and flocksâ€,

Ph.D Thesis, The Aligarh Muslim University, India, 1970.

N. Stevanovic and P.V. Protic, Abel-grassmann’s bands,

Quasigroups and Related Systems, vol. 11, no. 1, pp. 95–101,

M. Shah, T. Shah and A. Ali, “On the cancellativity of AGgroupoidsâ€, International Mathematical Forum, vol. 6, no. 44, pp.

–2194, 2011.

N. Stevanovic and P. V. Protic, Composition of Abel-Grassmann’s

-bands, Novi Sad J. Math. vol. 34, no. 2, pp.175 – 182, 2004.

J. R. Cho, Pusan, J. Jezek and T. Kepka, Paramedial Groupoids,

Czechoslovak Mathematical Journal, vol. 49, 277-290, 1996.

M. Shah, “A theoretical and computational investigations of AGgroupsâ€, PhD thesis, Quaid-i-Azam University, Islamabad, 2012.

A. Distler and M. Shah, V. Sorge, Enumeration of AG-groupoids,

Lecture notes in computer science, vol. 6824, pp. 1-14, 2011.

M. A. Kazim and M. Naseerudin, On almost semigroups,

Portugaliae Mathematica, vl.36, no. 1, 41-47, 1977.

J. M. Howie, “Fundamentals of Semigroup Theoryâ€, Clarendon

Press, Oxford, 2003.

M. Shah, I. Ahmad and A. Ali, “Discovery of new classes of AGgroupoidsâ€, Research Journal of Recent Sciences, vol. 1 no. 11, pp.

-49, 2012.

M. Shah, I. Ahmad and A. Ali, “On introduction of new classes of

AG-groupoidsâ€, Research Journal of Recent Sciences, vol. 2, no. 1,

p. 67-70, (2013).

Amanullah, M. Rashad, I. Ahmad and M. Shah, “On Modulo AGgroupoidsâ€, Journal of Advances in Mathematics, vol. 8, no. 3, pp.

-1613, 2014.

M. Rashad, I. Ahmad, Amanullah and M. Shah, “On relations

between right alternative and nuclear square AG-groupoidsâ€, Int.

Math. Forum, vol. 8, no. 5, pp. 237-243, 2013.

M. Rashad, I. Ahmad, M. Shah and Z. A. Khuhro, “Left Transitive

AG-groupoidsâ€, Sindh University Research Journal, Sci. Ser. vol.

, no. 4, p. 547-552, 2014.

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Published

21-09-2015

How to Cite

[1]
M. Shah and I. Ahmad, “Paramedial and Bol* Abel-Grassmann Groupoids”, The Nucleus, vol. 52, no. 3, pp. 130–137, Sep. 2015.

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