(2) Let n be an ordinal number, T be an admissible connected term order of n, L be an addassociative right complementable right zeroed commutative associative well unital distributive Abelian field-like non degenerated non empty double loop structure, and f , p, g be polynomials of n, L. Suppose f reduces to g, p, T . Then there exists a monomial m of n, L such that g = f −m∗ p and HT(m∗ p,T ) ...

We deene the notion of weak relative pseudo-complement, and we show that, for an arbitrary lattice, the property of weak relative pseudo-complementation is strictly weaker than relative pseudo-complementation, but stronger than pseudo-complementation. Our main interest for this notion is in relation with the theory of closure operators. We prove that if a complete lattice L is completely inf-di...

We characterize the distributive lattices of Jacobson rings and prove that if a semiring is a distributive lattice of Jacobson rings, then, up to isomorphism, it is equal to the subdirect product of a distributive lattice and a Jacobson ring. Also, we give a general method to construct distributive lattices of Jacobson rings.

Through an analysis of two different types of floating numeral quantifier (FNQ) constructions in Japanese, the present paper investigates the distributive and non-distributive interpretation in Japanese. Discussion of the interpretative issues related to ambiguity and intonation has indicated that FNQs are potentially ambiguous, offering both distributive and non-distributive readings.

The free distributive completion of a partial complete lattice is the complete lattice that it is freely generated by the partial complete latticèin the most distributive way'. This can be described as being a universal solution in the sense of universal algebra. Free distributive completions generalize the constructions of tensor products and of free completely distributive complete lattices o...

We consider superfluous elements in a bounded lattice with 0 and 1, introduce various types of graphs associated these elements. The notions such as element graph (S(L)), join intersection (JI(L)) lattice, distributive (SI(L)) are defined. Dual atoms play an important role to find connections between the lattice-theoretic properties those corresponding graph-theoretic properties. Consequently, ...

According to Chajda and Eigenthaler ([1]), a d-lattice is a bounded lattice L satisfying for all a, c ∈ L the implications (i) (a, 1) ∈ θ(0, c) → a ∨ c = 1; (ii) (a, 0) ∈ θ(1, c) → a ∧ c = 0; where θ(x, y) denotes the least congruence on L containing the pair (x, y). Every bounded distributive lattice is a d-lattice. The 5-element nonmodular lattice N 5 is a d-lattice. Theorem 1 A bounded latti...

Let L be a completely distributive lattice and C a topological construct; a process is given in this paper to obtain a topological construct C(L), called the tower extension of C (indexed by L). This process contains the constructions of probabilistic topological spaces, probabilistic pretopological spaces, probabilistic pseudotopological spaces, limit tower spaces, pretopological approach spac...

Given an integral commutative residuated lattices L=(L,∨,∧), its full twist-product (L2,⊔,⊓) can be endowed with two binary operations ⊙ and ⇒ introduced formerly by M. Busaniche R. Cignoli as well C. Tsinakis A. Wille such that it becomes a lattice. For every a∈L we define certain subset Pa(L) of L2. We characterize when is sublattice the (L2,⊔,⊓). In this case together some natural antitone i...