Cardinality and idempotency of partial one-one convex and contraction transformation semi group
Adeniji Adeniji · African Journal of Mathematics and Computer Science Research · 2013
Let Xn be a set with finite number of elements following natural ordering of numbers. The formulae for the total number of elements in partial one – one convex and contraction transformation semigroup and its idempotents are obtained and discussed in this paper. The relationship between fix α and idempotency is obtained and stated; an element α is an idempotent if |Imα |= |ƒ (α) |. Also, idempotents commute and the product of two or more idempotents is an idempotent. An element y is said to be unique if x is an invertible element such that xy = yx = 1, x, y S. Key words: Convex, contraction, fix element, idempotent and partial one – one transformation semigroup.