Transformation Semigroup of Alternating Nonnegative Integers
- 1 Department of Mathematics, Faculty of Science, University of Abuja, Abuja, Nigeria
- 2 Department of Mathematics, Faculty of Science, University of Abuja, Abuja, Nigeria
Abstract
Set of integers, Z n is split into even-odd parts. The even part is arranged in ways, while the odd part fixes one point at a time to compliment the even part thereby forming the semigroup, AZ n . Thus, -spaces are filled choosing maximum of two even points at a time. Green’s relations have formed important structures that enhance the algebraic study of transformation semigroups. The semigroup of Alternating Nonnegative Integers for n -even ( AZ n - even ) is shown to have only two D-classes, and there are -classes for n ≥4 . The cardinality of L-classes is constant. Certain cardinalities and some other properties were derived. The coefficients of the zigzag triples obtained are 1, and . The second and third coefficients can be obtained by zigzag addition.
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