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Let $L$ be a complete lattice with an involution operation $*$ (a unary operation such that for any $x, y \in L$, $x \leq y$ implies $x^{*} \geq y^{*}$). Now, suppose that there is an element of $L$ t …

Given a complete bounded lattice $L$, what do we know about the possibility of defining an addition operation $+$ that, broadly speaking, behaves like arithmetical addition? By this, I mean that as we …

Let $L_{1}$ and $L_{2}$ be non-isomorphic finite lattices of the same cardinality. Can there exist any lattice homomorphisms between $L_{1}$ and $L_{2}$?

When does an orthomodular lattice $L$ of projections onto a given Hilbert space have a non-trivial centre $Z(L)$ and what can we generally say about the cardinality of $Z(L)$?

Is there a natural way to define the 'distance' between two Boolean algebra homomorphisms $f, g: B \rightarrow B'$? I'm thinking of something like the Kullback leibeler divergence for probability func …