In 1999, for lattices A and B, G. Grtzer and F. Wehrung introduced the lattice tensor product, A⊠B. In Part I of this paper, we showed that for a finite lattice A and a bounded lattice B, this construction can be "coordinatized,'' that is, represented in BA so that the representing elements are easy to recognize. In this note, we show how to extend our method to an arbitrary bounded
lattice A to coordinatize A⊠B.
G. Grtzer and F. Wehrung has recently introduced the lattice tensor product, A⊠B, of the lattices A and B. In this note, for a finite lattice A and an arbitrary lattice B, we compute the ideal lattice of A⊠B, obtaining the isomorphism Id(A⊠B)≌A⊠Id B. This generalizes an earlier result of G. Grtzer and F. Wehrung proving this isomorphism for A = M_3 and Bn-modular. We prove this isomorphism by utilizing the coordinatization of A⊠B introduced in Part I of this paper.
G. Grtzer and F. Wehrung introduced the lattice tensor product, A⊠B, of the lattices Aand B. In Part I of this paper, we showed that for any finite lattice A, we can "coordinatize" A⊠B, that is, represent A⊠,B as a subset A<B> of BA, and provide an effective criteria to recognize the A-tuples of elements of B that occur in this representation. To show the utility of this coordinatization, we prove, for a finite lattice A and a bounded lattice B, the isomorphism Con A<B> ≌ (Con A)<Con B>, which is a special case of a recent result of G. Grtzer and F. Wehrung and a generalization of a 1981 result of G. Grtzer,
H. Lakser, and R.W. Quackenbush.
References  Davey , B. A . and Priestley , H. A . Introduction to Lattices and Order . Cambridge University Press , Cambridge , 2002 . Second edition .  Dilworth , R. P . A decomposition theorem for partially ordered sets
Authors:Liviu-Constantin Holdon and Arsham Borumand Saeid
References  A . Borumand Saeid and M . Pourkhatoun . Obstinate filters in residuated lattices . Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie , 55 ( 4 ): 413 – 422 , 2012 .  D . Buşneag , D . Piciu and
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.