有限分配格的自同态半群

ENDOMORPHISM SEMIGROUPS OF A FINITE DISTRIBUTIVE LATTICE

设 P 是有限偏序集,L 是有限分配格.它们分别对应有限分配格P~*=Hom_(POS)(P,2) 及有限偏序集 L~*=Hom_(DL)(L(?)2) 。并且 L~*(序)反同构于 L的联既约元集,L^(**)(格)同构于 L.本文证明了对于有限配格 L,End_(DL)L 反同构于 End_(POS)L~*。进而得到 End_(DL)L 反同构于 End_(POS)P,其中 P 表 L 的联既约元集.作为推论,也可以获得有限 Boolc 代数情形的相应结论.

For a finite partially ordered set Pand αfinite distributive lattice L,P~*=Hom_(POS)(P,2) and L~*=Hom_(DL)(L,2) are corresponding finite distributive lattice and finite partially or- dered set,respectively.It is known that L~* is anti-isomorphic to the set of join-irreducible elements of L,and L^(**)is isomorphic to L.In this paper,it is shown that for the finite dis- tributive lattice L,End_(DL)Lis anti-isomorphic to End_(POS)L~*,and hence,End_(DL)Lis anti-isomorphic to End_(POS)P,where Pis the set of join-irreducible elements of L.