Join Irreducible Pseudovarieties, Group Mapping, and Kovács-Newman Semigroups
نویسندگان
چکیده
We call a pseudovariety finite join irreducible if V ≤ V1 ∨V2 =⇒ V ≤ V1 or V ≤ V2. We present a large class of group mapping semigroups generating finite join irreducible pseudovarieties. We show that many naturally occurring pseudovarieties are finite join irreducible including: S, DS, CR, CS and H, where H is a group pseudovariety containing a non-nilpotent group.
منابع مشابه
Join irreducible semigroups
We begin a systematic study of those finite semigroups that generate join irreducible members of the lattice of pseudovarieties of finite semigroups, which are important for the spectral theory of this lattice. Finite semigroups S that generate join irreducible pseudovari-eties are characterized as follows: whenever S divides a direct product A × B of finite semigroups, then S divides either A ...
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