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This short note reviews the main contributions of the Ph.D. thesis
of Imre Simon.
His graduate work had major impact on algebraic theory of automata
and thirty years later we are in a good position to appreciate
how sensitive he was in selecting good problems, and how clever in
We find the atoms of certain subclasses of varieties of finite semigroups and the corresponding varieties of languages. For example we give a new description of languages whose syntactic monoids are R-trivial and idempotent. We also describe the least variety containing all commutative semigroups and at least one non-commutative semigroup. Finally we extend to varieties of finite semigroups some classical results about semilattice decomposition of semigroups.
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