▁two ▁vari eties ▁is ▁their ▁intersection ▁and ▁the ▁join ▁of ▁two ▁vari eties ▁is ▁the ▁smallest ▁variety ▁that ▁contains ▁both ▁of ▁them . ▁The ▁complete ▁structure ▁of ▁this ▁lattice ▁is ▁known ; ▁in ▁particular , ▁it ▁is ▁count able , ▁complete , ▁and ▁distrib utive . ▁ ▁The ▁sub l attice ▁consisting ▁of ▁the ▁ 1 3 ▁vari eties ▁of ▁regular ▁bands ▁is ▁shown ▁in ▁the ▁figure . ▁ ▁The ▁vari eties ▁of ▁left - zero ▁bands , ▁sem il att ices , ▁and ▁right - zero ▁bands ▁are ▁the ▁three ▁atoms ▁( non - t rivial ▁minimal ▁elements ) ▁of ▁this ▁lattice . ▁ ▁Each ▁variety ▁of ▁bands ▁shown ▁in ▁the ▁figure ▁is ▁defined ▁by ▁just ▁one ▁identity . ▁ ▁This ▁is ▁not ▁a ▁coinc idence : ▁in ▁fact , ▁every ▁variety ▁of ▁bands ▁can ▁be ▁defined ▁by ▁a ▁single ▁identity . ▁ ▁See ▁also ▁Boolean ▁ring , ▁a ▁ring ▁in ▁which ▁every ▁element ▁is ▁( multip lic atively ) ▁ide mp ot ent ▁Now here ▁commut ative ▁sem igr oup ▁Special ▁classes ▁of ▁sem igr oups ▁Orth odox ▁sem igr oup ▁ ▁Notes ▁ ▁References ▁. ▁. ▁. ▁. ▁. ▁. ▁. ▁. ▁. ▁. ▁ ▁Category : Al gebra ic ▁structures ▁Category : Sem igr oup ▁theory <0x0A> </s> ▁The ▁ 2 0 0 9 ▁Sh iz u oka ▁earth qu ake ▁occurred ▁with ▁a ▁magnitude ▁of ▁ 6 . 4 ▁ ▁that ▁hit ▁Sh iz u oka ▁Pref ect ure ▁in ▁the ▁south ▁of ▁H ons h ū ,