African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 254

Short Communication

Cardinality and idempotency of partial one-one convex and contraction transformation semi group

Adeniji, A. O.
  • Adeniji, A. O.
  • Department of Mathematics, Faculty of Science, University of Abuja, Nigeria
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  •  Accepted: 10 May 2013
  •  Published: 31 May 2013

Abstract

 

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.