A Characterization of (2,n)-Semigroup ofn-Place Functions and De Morgan (2,n)-Semigroup ofn-Place Functions

De Morgan (2,n)-Semigroups ofn-Place Functions

“…Abstract characterizations of algebras T A n A ⊕ 1 ⊕ n and T A n A ⊕ 1 ⊕ n ¯ I 1 I n , where I i a 1 a n = a i , one can find in [4] and [5]. Below, we present an abstract characterization of the De Morgan Menger 2 n -semigroup of n-place functions.…”

“…We limit ourselves to the proof of sufficiency because the necessity of (3)-(10) one can find in [1][2][3][4]. 1 Let all the conditions of the theorem be satisfied by G. Consider the set G * = G ∪ e 1 e n , where e 1 e n are different elements not belonging to G. For every g ∈ G, we define on G * an n-place function * g putting *…”

“…[3]); • The Mann's superposition ⊕ i (1 ≤ i ≤ n) defined by f ⊕ i g a 1 a n = f a 1 a i−1 g a 1 a n a i+1 a n (2) for all f g ∈ F A n A and a 1 a n ∈ A, where the left and right hand sides of (2) are defined, or not defined, simultaneously (cf. [3,4]); • The quasicomplementation (the opposite operation) of f ∈ F A n A defined bȳ f a 1 a 2 a n = f a n a 2 a 1 Since all superpositions ⊕ Morgan Menger 2 n -semigroups of n-place functions (cf. [4,5]).…”

“…[3,4]); • The quasicomplementation (the opposite operation) of f ∈ F A n A defined bȳ f a 1 a 2 a n = f a n a 2 a 1 Since all superpositions ⊕ Morgan Menger 2 n -semigroups of n-place functions (cf. [4,5]). In the case when all elements of the set are full n-place functions, we say that this algebra is a De Morgan Menger 2 n -semigroup of full n-place functions.…”