一类完全正则半群簇子簇格的性质

Properties of a Class of Lattice of Subvarieties of Variety of Completely Regular Semigroups

本文研究了完全正则半群簇的子簇格［Ｖ＋∩ＰＶ，Ｖ＋∩ＰＶ］的某些格运算性质，我们证明了簇Ｖ＋∩ＰＶ可分解为Ｖ与Ｖ＋∩ＰＶ的并；对任意完全正则半群簇Ｗ，有Ｗ∩（Ｖ∨Ｖ＋∩ＰＶ）＝（Ｗ∩Ｖ）∨（Ｗ∩Ｖ＋∩ＰＶ）．特别地，我们得到了等式Ｖ＋∩ＰＶ＝Ｖ成立的若干条件．

In this paper, some lattice theoretical properties of the lattice [V +∩PV, V +∩PV] are studied. It is proved that V +∩PV is the join of V and V +∩PV and W∩ (V∨V +∩PV)= (W∩ V)∨(W∩V +∩PV) for all varieties W, V of completely regular semigroups. In particular, some conditions for the equation V +∩PV =V to be true are obtained.