Representation theorem for finite quasi-boolean algebras
Representations of finite lattices by orders on finite sets
Representations of locally distributive lattices
Representing Upper Probability Measures over Rational Lukasiewicz Logic.
Residuation in twist products and pseudo-Kleene posets
M. Busaniche, R. Cignoli (2014), C. Tsinakis and A. M. Wille (2006) showed that every residuated lattice induces a residuation on its full twist product. For their construction they used also lattice operations. We generalize this problem to left-residuated groupoids which need not be lattice-ordered. Hence, we cannot use the same construction for the full twist product. We present another appropriate construction which, however, does not preserve commutativity and associativity of multiplication....
Residuation Theory (Book Review by R. McFadden.
Reticulation of a 0-distributive Lattice
A congruence relation on a 0-distributive lattice is defined such that the quotient lattice is a distributive lattice and the prime spectrum of and of are homeomorphic. Also it is proved that the minimal prime spectrum (maximal spectrum) of is homeomorphic with the minimal prime spectrum (maximal spectrum) of .
Retractive MV-algebras.
Retracts and Q-independence
A non-empty set X of a carrier A of an algebra A is called Q-independent if the equality of two term functions f and g of the algebra A on any finite system of elements a₁,a₂,...,aₙ of X implies f(p(a₁),p(a₂),...,p(aₙ)) = g(p(a₁),p(a₂),...,p(aₙ)) for any mapping p ∈ Q. An algebra B is a retract of A if B is the image of a retraction (i.e. of an idempotent endomorphism of B). We investigate Q-independent subsets of algebras which have a retraction in their set of term functions.
Riemann average truth-value of Łukasiewicz formulas
Rings in Post algebras.