正则纯整群带的算子半群和同余网

Operator Semigroups and Networks of Congruences for Regular Orthocryptogroups

正则半群Ｓ的同余格（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．我们确定了所有正则纯整群带的同余格上由Ｋ，ｋ，Ｔ和ｔ生成的算子半群．并确定了正则纯整群带上任意同余的同余网．

Four operators K,k,T and t are defined on the congruence lattice S of 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. We determine the semigroup generated by operators K,k,T and t as they act on congruence lattices of all regular orthocryptogroups. We also determine the network of congruences associated with a congruence ρ∈S.