论文信息 - Joins of minimal quasivarieties

Joins of minimal quasivarieties

LetL(K) denote the lattice (ordered by inclusion) of quasivarieties contained in a quasivarietyK and letD2 denote the variety of distributive (0, 1)-lattices with 2 additional nullary operations. In the present paperL(D2) is described. As a consequence, ifM+N stands for the lattice join of the quasivarietiesM andN, then minimal quasivarietiesV0,V1, andV2 are given each of which is generated by a 2-element algebra and such that the latticeL(V0+V1), though infinite, still admits an easy and nice description (see Figure 2) while the latticeL(V0+V1+V2), because of its intricate inner structure, does not. In particular, it is shown thatL(V0+V1+V2) contains as a sublattice the ideal lattice of a free lattice with ω free generators. Each of the quasivarietiesV0,V1, andV2 is generated by a 2-element algebra inD2.

M. E. Adams | W. Dziobiak

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