Loubere IMagic Squares Semigroups and Groups

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Babayo A.M.
Babayo A.M.
2
G.U.Garba
G.U.Garba
1 Federal University Kashere

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This work is a pioneer investigation of semigroups and groups over the Loubéré Magic Squares. By the Loubéré Magic Squares, we understand the magic squares formed by the De La Loubéré Procedure. The set of the Loubéré Magic Squares equipped with the matrix binary operation of addition forms a semigroup if the underlining set so considered is the multi set of natural numbers; and if we consider the multi set of integer numbers as the underlined set of entries of the square, the set of the squares enclosed with the aforementioned operation forms an abelian group. The Loubéré Magic Squares are always recognized with centre piece C and magic sum M(S). We showcase that the set of the centre pieces and the set of the magic sums form respective abelian groups if both are equipped with integer numbers operation of addition. We also explicate that the set of the eigen values of the squares enclosed with the integer addition (operation) forms an abelian group. We reveal that the subelement (a terminology we introduced) Magic Squares of the Loubéré Magic Squares forms a semigroup and the Subelement Magic Squares of the Loubéré Magic Squares Group forms a group, with respect to the matrix binary operation of addition.

4 Cites in Articles

References

  1. Daryl Stephens (1993). Matrix Properties of Magic Squares.
  2. C Lee,Sallows (1986). Health hazard evaluation report: HETA-86-277-1750, Project Orbis, Inc., New York, New York..
  3. John Howie (2003). Fundamentals of Semigroup Theory.
  4. Joseph Rotman (2015). A First Course in Abstract Algebra.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

Babayo A.M.. 2015. \u201cLoubere IMagic Squares Semigroups and Groups\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 15 (GJSFR Volume 15 Issue F1): .

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Issue Cover
GJSFR Volume 15 Issue F1
Pg. 61- 70
Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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GJSFR-F Classification: MSC 2010: 16W22
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v1.2

Issue date

February 6, 2015

Language

English

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This work is a pioneer investigation of semigroups and groups over the Loubéré Magic Squares. By the Loubéré Magic Squares, we understand the magic squares formed by the De La Loubéré Procedure. The set of the Loubéré Magic Squares equipped with the matrix binary operation of addition forms a semigroup if the underlining set so considered is the multi set of natural numbers; and if we consider the multi set of integer numbers as the underlined set of entries of the square, the set of the squares enclosed with the aforementioned operation forms an abelian group. The Loubéré Magic Squares are always recognized with centre piece C and magic sum M(S). We showcase that the set of the centre pieces and the set of the magic sums form respective abelian groups if both are equipped with integer numbers operation of addition. We also explicate that the set of the eigen values of the squares enclosed with the integer addition (operation) forms an abelian group. We reveal that the subelement (a terminology we introduced) Magic Squares of the Loubéré Magic Squares forms a semigroup and the Subelement Magic Squares of the Loubéré Magic Squares Group forms a group, with respect to the matrix binary operation of addition.

This work is a pioneer investigation of semigroups and groups over the Loubéré Magic Squares. By the Loubéré Magic Squares, we understand the magic squares formed by the De La Loubéré Procedure. The set of the Loubéré Magic Squares equipped with the matrix binary operation of addition forms a semigroup if the underlining set so considered is the multi set of natural numbers; and if we consider the multi set of integer numbers as the underlined set of entries of the square, the set of the squares enclosed with the aforementioned operation forms an abelian group. The Loubéré Magic Squares are always recognized with centre piece C and magic sum M(S). We showcase that the set of the centre pieces and the set of the magic sums form respective abelian groups if both are equipped with integer numbers operation of addition. We also explicate that the set of the eigen values of the squares enclosed with the integer addition (operation) forms an abelian group. We reveal that the subelement (a terminology we introduced) Magic Squares of the Loubéré Magic Squares forms a semigroup and the Subelement Magic Squares of the Loubéré Magic Squares Group forms a group, with respect to the matrix binary operation of addition.

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Loubere IMagic Squares Semigroups and Groups

Babayo A.M.
Babayo A.M. Federal University Kashere
G.U.Garba
G.U.Garba

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