A set-theoretical representation for weakly idempotent lattices and interlaced weakly idempotent bilattices. (English) Zbl 1402.06001
Summary: We give set-theoretical characterizations both for weakly idempotent lattices and interlaced weakly idempotent bilattices. In particular, we obtain a set-theoretical representation for interlaced bilattices and distributive bilattices (without bounds).
MSC:
| 06B05 | Structure theory of lattices |
| 06B75 | Generalizations of lattices |
| 06D05 | Structure and representation theory of distributive lattices |
| 06D75 | Other generalizations of distributive lattices |
| 03G10 | Logical aspects of lattices and related structures |
| 08B05 | Equational logic, Mal’tsev conditions |
| 08B25 | Products, amalgamated products, and other kinds of limits and colimits |
Keywords:
weakly idempotent semilattice; weakly idempotent lattice; weakly idempotent bilattice; filter and ideal of weakly idempotent lattice; filter and ideal of weakly idempotent bilatticeReferences:
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