Abstract
By previous results of Putcha and the author, an irreducible algebraic monoid M is regular if and only if the Zariski closure R(G) ⊆ M is completely regular, where R( G) is the solvable radical of G. Thus, the classification problem leads initially to extreme cases; reductive monoids and completely regular monoids with solvable unit groups. In this paper we classify normal, completely regular (NCR) monoids with solvable unit group. It turns out that each NCR monoid M is determined by its unit group G = TU and the closure Z of T in M. For the converse, we find the exact conditions on a diagram T ̄ =Z↩T↪G for which there exists an NCR monoid M with Z= T ̄ ⊂M .
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