On Independence and Minimal Generating Set in Semigroups and Countable Systems of Semigroups.

Författare

  • Marshal Imeh Sampson Akwa Ibom State University, Ikot Akpaden
  • LIPCSEY ZSOLT Department of Mathematics, University of Calabar, Calabar, CRS, Nigeria
  • Jonas Ogar ACHUOBI Department of Mathematics, University of Calabar, Calabar, CRS, Nigeria
  • CHRISTIANA IGIRI Department of Mathematics, University of Calabar, Calabar, CRS, Nigeria
  • LOUIS Effiong ESSIEN Department of Mathematics, Abia State Polytechnic, Aba, Nigeria

Nyckelord:

Minimal, maximal, minimum, maximum, Generating Set, Semigroup, Ordering, Independence, countable systems

Abstract

This paper studies independence in semigroup by exploring the relationship between the concepts of “minimal generating set” as compared to “minimum generating set” using comparability of elements, as induced by the orderings on the semigroup. It is shown that minimal generating set implies independence and vice versa. Two concluding results which are algorithms respectively for determining minimal generating sets for countable systems of semigroups and for any given semigroup, are given.

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Publicerad

2023-10-31

Referera så här

Sampson, M. I., ZSOLT, L., ACHUOBI, J. O., IGIRI, C., & ESSIEN, L. E. (2023). On Independence and Minimal Generating Set in Semigroups and Countable Systems of Semigroups. International Journal of Mathematical Analysis and Modelling, 6(2). Hämtad från https://tnsmb.org/journal/index.php/ijmam/article/view/89

Nummer

Vol 6 Nr 2 (2023): Volume 6, Issue 2 (Oct. - Nov. 2023)

Sektion

Articles