纯正群并半群簇和密码群并半群簇的上确界

The Join of Orthogroup Variety and Cryptogroup Variety

在完全正则半群簇的子簇格中,首先用等式((x0y0)0z0)0=(x0(y0z0)0)0定义了一个子簇,并举例说明它是完全正则半群簇的真子簇,追加等式x(yz)0x(yz)0=(yz0)0x(yz)0和(xy)0z(xy)0z=(xy)0z(x0y)0z,定义前一子簇的又一子簇,并举例说明这3个等式相互独立,证明了这3个等式恰好给出了纯正群并半群簇和密码群并半群簇的上确界.

A subvariety of the variety of completely regular semigroups is defined by the identity（（x0y0）0z0）0 =（x0（y0z0）0）0.An example is provided to illustrate that the subvariety is proper.Two additional identities,x（yz）0x（yz）0=（yz0）0x（yz）0and（xy）0z（xy）0z=（xy）0z（x0y）0z,are used to define a subvariety of the above subvariety.Examples are given to show that the above three identities are independent on each other.It is proved that the proper subvariety defined by the three identities is the join of the orthogroup variety and the cryptogroup variety.