The purpose of this paper is to provide a proper identification of normal irreducible, regular algebraic monoids. The results from the work of Renner [3,4] suggest that we should be able to find a classification of these monoids in terms of their unit groups, and related toroidal data. That is what we accomplish here.
Keywords: Unipotent radical, . toroidal data, normal, irreducible, regular, zero element, maximal torus, Zariski closure, Lie algebra
Journal of the Nigerian Association of Mathematical Physics, Volume 19 (November, 2011), pp 37 – 40