-Lattices of varieties of algebras of different types
We introduce the concept of vague ideals in a distributive implication groupoid and investigate their properties. The vague ideals of a distributive implication groupoid are also characterized.
It is well-known that there exist infinite modular lattices possessing no non-trivial valuations. In this paper a class of modular lattices is defined and it is proved that each lattice belonging to has a nontrivial valuation. Next, a result of . Birkhoff concerning valuations on modular lattices of finite length is generalized.
A rotational lattice is a structure where is a lattice and is a lattice automorphism of finite order. We describe the subdirectly irreducible distributive rotational lattices. Using Jónsson’s lemma, this leads to a description of all varieties of distributive rotational lattices.
We give an equational description of all idempotent groupoids with at most three essentially n-ary term operations.