In this paper, we introduce the notions of Belluce lattice associated with a bounded $BCK$-algebra and reticulation $BCK$-algebra. To do this, first, define operations $curlywedge ,$ $curlyvee $ $sqcup on $BCK$-algebras study some algebraic properties them. Also, for $A$ Zariski topology Spec(A)$ induced $tau _{A,Max(A)}$ $Max(A)$. We prove $(Max(A),tau_{A,Max(A)})$ is compact topological space...

The ordinal sum construction provides a very effective way to generate new triangular norm on the real unit interval from existing ones. One of most prominent theorems concerning norms states that is continuous if and only it uniquely representable as an Archimedean norms. However, subintervals bounded lattice not always (even one summand involved), just extends in naïve way. In present paper, ...

It is shown that strict resolutions of Fn by F–limit groups have length bounded by 3n. As an application we show that the abelian analysis lattice of a limit group L has height bounded by 3 rk(L).

We establish a one to one correspondence between a set of certain bounded partitions and a set of two-rowed standard Young tableaux of skew shape. Then we obtain a formula for a number which enumerates these partitions. We give two proofs for this formula, one by applying the above correspondence, the other by using the reflection principle. Finally, we give another expression for this number i...

We generalize the symmetry on Young’s lattice, found by Suter, to a symmetry on the k-bounded partition lattice of Lapointe, Lascoux and Morse. Résumé. Nous généralisons la symmetrie sur le treillis de Young, découvert par Suter, à une symétrie sur le treillis des partages bornés par k et étudié par Lapointe, Lascoux and Morse.

In this paper, we define the concepts of fuzzy initial and final segments in an Almost Distributive Lattice (ADL) certain properties these are discussed. It is proved that set forms a complete lattice ADL A if only bounded distributive lattice.

By a lattice we shall always mean a distributive lattice which is bounded, i.e. has both a bottom element 0 and a top element 1. Lattice homomorphisms will always be assumed to preserve 0 and 1. By a modality on a (distributive) lattice L = (L, ∧, ∨, ≤, 0, 1) is meant a map : L → L satisfying (1) 1 = 1, (2) (x ∧ y) = x ∧ y for x, y ∈ L. The pair (L, ) will be called a modalized (distributive) l...