Abstract

In this study we have constructed various AG-groupoids from vector spaces over finite fields and also from finite fields by defining new operations on these structures.

Keywords:

AG-groupoid, Cayley diagram, Galois field,

References

1. Holgate, P., 1992. Groupoids satisfying a simple invertive law. Math. Stud., 61(1-4): 101-106.
   
2. Kazim, M.A. and M. Naseeruddin, 1972. On almost semigroups. Alig. Bull. Math., 2: 1-7.
   
3. Mushtaq, Q. and S.M. Yusuf, 1978. On LA-semigroups. Alig. Bull. Math., 8: 65-70.
   
4. Mushtaq, Q. and S.M. Yusuf, 1988. On LA-semigroup defined by a commutative inverse semigroup. Math. Bech., 40: 59-62.
   
5. Mushtaq, Q. and Q. Iqbal, 1990. Decomposition of a locally associative LA-semigroup. Semigroup Forum, 41: 154-164.
   CrossRef    
6. Protic, P.V. and N. Stevanovic, 2004. Abel-Grassmann's bands. Quasigroups Relat. Syst., 11: 95-101.
   
7. Stevanovic, N. and P.V. Protic, 2004. Composition of Abel-Grassmann's 3-bands. Novi Sad. J. Math., 34(2): 175-182.
   

Competing interests

The authors have no competing interests.

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The authors have no competing interests.