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. C ., and Koh , K. M . On the length of the lattice of sublattices of a finite distributive lattice . Algebra Universalis 15 , 2 ( 1982 ), 233 – 241 . [6] Chen , C. C ., Koh , K. M ., and Teo , K. L . On the sublattice-lattice of a
This paper is connected with the fundamental work of E.S. Barnes and G.E. Wall [1] in which the authors defined the so-called Barnes-Wall lattice. We shall determine the number of minima of some special sublattices of dimension 2 n -k of this lattice, where 1=k=n.
The class CR of completely regular semigroups considered as algebras with binary multiplication and unary operation of inversion forms a variety. Kernel, trace, local and core relations, denoted by K, T, L and C, respectively, are quite useful in studying the structure of the lattice L(CR) of subvarieties of CR. They are equivalence relations whose classes are intervals. Their ends are used for defining operators on L(CR).
Starting with a few band varieties, we repeatedly apply operators induced by upper ends of classes of these relations and characterize corresponding classes up to certain variety low in the lattice L(CR). We consider only varieties whose origin are “central” band varieties, that is those in the middle column of the lattice L(B) of band varieties. Several diagrams represent the (semi)lattices studied.
Abstract
Using Mössbauer spectroscopy the quinolinates of iron/II/ and iron/III/ have been studied. In iron/II/ quinolinate three sublattices were evidenced, two of them being attributed to Fe2+ ions and the third to Fe3+ impurities. In the iron/III/ quinolinate five structural sublattices were found, two of them containing Fe3+ ions, the other two Fe2+ ions and the fifth may be attributed to the interstitial Fe3+ ions.
Abstract
Oxidation-reduction reactions were studied for the following oxocuprates: LiCuO, Li2CuO2, SrCu2O2, Sr2CuO3, SrCuO2, BaCu2O2, BaCuO2,LaCuO2, La2CuO4, Ca2CuO3 and Bi2CuO4. Transformation schemes have been proposed for the anionic sub-lattices of these salts and the effect of cations on the properties of the anionic sub-lattices in oxidation-reduction reactions was determined.
