Motivated by cryptography, permutations induced by polynomial functions on finite lattices L = (L, ∨, ∧, *) with an antitone involution * are investigated. These permutations together with the operation of composition form a subgroup of the symmetric group on L. We describe the structure of this subgroup for different classes of lattices L and indicate… (More)
Ring-like operations are introduced in pseudocomplemented semi-lattices in such a way that in the case of Boolean pseudocomplemented semilattices one obtains the corresponding Boolean ring operations. Properties of these ring-like operations are derived and a characterization of Boolean pseudocomplemented semilattices in terms of these operations is given.… (More)
The relationship between MV-algebras and semirings was described by A. Di Nola and B. Gerla (). Since commutative basic algebras are similar to MV-algebras up to associativity of the binary operation we try to get a similar relationship between commutative basic algebras and so-called near semirings and we show that this is possible. This means that… (More)
We generalize the one-to-one correspondence between Boolean algebras and Boolean rings to so-called difference lattices and commutative strong difference ring-like algebras. Moreover, we show that difference ring-like algebras induce some sort of symmetric difference in corresponding posets.