TITLE:
Transformation Semigroup of Alternating Nonnegative Integers
AUTHORS:
Adenike Olusola Adeniji, Janet Ifiok Obafemi
KEYWORDS:
Green’s Relations, Partial Order Relation, Idempotents, Band, Generator
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.12 No.11,
November
7,
2022
ABSTRACT: Set of integers, Zn 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, AZn. 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 (AZn-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.