Revisiting Characterization of Semigroups: Exploring limitations of Independence

Resumen

This paper reviews the evaluation of the characterization of semigroups Independence, generating systems  by Sampson, M. I. (see [2]), which began with studying the work of Howie and Ribeiro (see [1]) to investigate the effect of the concept of independence on semigroup generating systems. While independence is often considered fundamental in determining minimal generators for semigroups, we show instances where this notion proves inadequate. Specifically, with illustrated variations in the role of independence in Semigroup as compared to vector spaces. The study shows reliable characterization of independent generating sets that helps in the selection algorithm for the basis elements of any given semigroups.