Residuated operators in complemented posets

Orthomodular Posets Can Be Organized as Conditionally Residuated Structures

It is proved that orthomodular posets are in a natural one-to-one correspondence with certain residuated structures.

Modal operators for meet-complemented lattices

Noncommutative Pieri Operators on Posets

We consider graded representations of the algebra NC of noncommutative symmetric functions on the Z-linear span of a graded poset P . The matrix coefficients of such a representation give a Hopf morphism from a Hopf algebra HP generated by the intervals of P to the Hopf algebra of quasi-symmetric functions. This provides a unified construction of quasi-symmetric generating functions from differ...

Reducts and Modal Operators on Residuated Lattices

Proposition 3. If A=〈A,∧,∨, ·, \, /, 1, γ〉 is a residuated lattice with a nucleus γ, then the algebra Aγ=〈Aγ ,∧,∨γ , ·γ , \, /, γ(1)〉 is a residuated lattice, where Aγ=γ[A] and for all x, y ∈ Aγ , x ∨γ y=γ(x ∨ y) and x ·γ y=γ(x · y). For a variety V of residuated lattices with modal operators, consider V∗, the full subcategory of V consisting of those pairs 〈B, 〉 such that B generates B as a re...

Pseudocomplements of closure operators on posets

Some recent results provide su,cient conditions for complete lattices of closure operators on complete lattices, ordered pointwise, to be pseudocomplemented. This paper gives results of pseudocomplementation in the more general setting of closure operators on mere posets. The following result is 0rst proved: closure operators on a meet-continuous meet-semilattice form a pseudocomplemented compl...