IIARD International Institute of Academic Research and Development

INTERNATIONAL JOURNAL OF APPLIED SCIENCES AND MATHEMATICAL THEORY (IJASMT )

E- ISSN 2489-009X
P- ISSN 2695-1908
VOL. 9 NO. 3 2023
DOI: https://doi.org/10.56201/ijasmt.v9.no3.2023.pg90.100

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Rank Of Some Semigroup

Udoaka Otobong G

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Abstract

A new computational technique for rank of some semigroup is presented. The technique is based on matrix representation and simplifies the computational efforts encountered using direct definition technique of computing ranks. The important of this idea for the study of abstract groups seems to depend on the fact that group-theoretical calculations are easier to carry out in groups of matrices than in abstract groups. Its effectiveness is demonstrated in the computation of the rank of certain transformation semigroup, symmetry semigroup (S3), Dihedral group (D4), monogenic semigroup and the inverse semigroup. The new technique has been further employed in the computation of rank of Markov semigroup, a semigroup which admits a prefix-closed regular language of unique representatives with respect to some generating set.

keywords:

Monoid, Transformation semigroup, Representation, Markov semigroup and Echelon matrix

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References:

ABDULAHI UMAR * (1996), ‘On the Rank of Certain Finite semigroup of order-decreasing
Transformation’, Portugaliae Mathematica vol.53 Fac.

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