Volume 17 | Number 1 | Year 2015 | Article Id. IJMTT-V17P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V17P505
This pioneer work explicates that the set of the Minimum Zero-Centre-Pandiagonal Composite Type II (a) Loubéré Magic Squares over Multi Set of Integer Numbers ZL(as we denote it) forms an additive abelian group if equipped with the matrix binary operation of addition (as we denote it) and if it is enclosed with the integer number operation of multiplication (as we denote it), it forms a multiplicative semigroup with identity. That is, forms a semiring for it satisfies all the axioms of a semiring.
[1] Maya Ahmed, “Algebraic Combinatorics of Magic Squares,” A Doctor of Philosophy Dissertation, University of California, Davis, pp. 85, 2004.
[2] Gan Yee Siang, Fon Wan Heng, Nor Haniza Sarmin, “Properties and Solutions of Magic Squares,” Menemui Matematik (Discovering Mathematics), vol. 34, pp. 69, 2012.
[3] John M. Howie, “Fundamentals of Semigroup Theory, Oxford University Press,” New York, United States, vol. 1, pp.1, 2003.
[4] Jonathan S.Golan, “Some Recent Applications of Semiring Theory,” International Conference on Algebra in Memory, Kostia Beidar, pp1-2, 2008.
Babayo A.M, Moharram Ali Khan, "Minimum Zero-Centre-Pandiagonal Composite Type II (a) Loubéré Magic Squares over Multi Set of Integer Numbers as a Semiring," International Journal of Mathematics Trends and Technology (IJMTT), vol. 17, no. 1, pp. 25-31, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V17P505