一类E-酉正则半群的TK-算子半群

TK-OPERATOR SEMIGROUPS FOR A CLASS OF E-UNITARY REGULAR SEMIGROUPS

正则半群S的同余格C(S)上的算子K、k、T和t定义如下,对于ρ∈S,ρK和ρk(ρT和ρt)分别是与ρ有相同核(迹)的最大和最小同余.对于同态像是E-酉的E-酉正则半群S,先确定了4个算子Γ={K,k,T,t}在同余格C(S)上满足的关系Σ,给出了商半群Γ+/Σ*,然后确定了这类半群的TK-算子半群是Γ+/Σ*的同态像.

Four operators K,k,T and t are defined on the congruence lattice C（S） on a regular semigroup S as follows,for ρ∈S,ρK and ρk（ρT and ρt） are the greatest and the smallest congruences with the same kernel（trace） as ρ,respectively.The relations satisfied by operators K,k,T and t are determined as they act on congruence lattices of all E-unitary regular semigroups with that all their homomorphic images are E-unitary,and the quotient semigroup Γ^＋/Σ^＊ is given.It is also determined that this TK-operator is a homomorphic image of Γ^＋/Σ^＊.