We study the algebra U ζ obtained via Lusztig's 'integral' form [Lu 1, 2] of the generic quantum algebra for the Lie algebra g = sl 2 modulo the two-sided ideal generated by K l − 1. We show that U ζ is a smash product of the quantum deformation of the restricted universal enveloping algebra u ζ of g and the ordinary universal enveloping algebra U of g, and we compute the primitive (= prime) id...

A lattice diagram is a finite set L = {(p1, q1), . . . , (pn, qn)} of lattice cells in the positive quadrant. The corresponding lattice diagram determinant is ∆L(Xn;Yn) = det ‖ x pj i y qj i ‖. The space ML is the space spanned by all partial derivatives of ∆L(Xn;Yn). We denote by M 0 L the Y -free component of ML. For μ a partition of n + 1, we denote by μ/ij the diagram obtained by removing t...

We present here constructions of ideals A of the poset of n-vectors (x1, ..., xn) with integer entries, ordered coordinatewise, on which the maximal and minimal values of Wφ(A) = ∑ x∈A φ( ∑n i=1 xi) are achieved for a given unimodal function φ. As a consequence we get a new approach to prove the well-known ClementsLindström Theorem [6].

In this paper, we introduce the notionofWajsberg implicative ideal(WI-ideal)of lattice Wajsberg algebra.Further, we definelattice H-Wajsberg algebra, implication homomorphismand lattice implication homomorphism oflattice Wajsberg algebra. Finally, we give kernel of implication homomorphism and obtain some oftheir properties.

We compute the monoid V (LK(E)) of isomorphism classes of finitely generated projective modules over certain graph algebras LK(E), and we show that this monoid satisfies the refinement property and separative cancellation. We also show that there is a natural isomorphism between the lattice of graded ideals of LK(E) and the lattice of order-ideals of V (LK(E)). When K is the field C of complex ...

The toric Hilbert scheme of a lattice L ⊆ Z is the multigraded Hilbert scheme parameterizing all ideals in k[x1, . . . , xn] with Hilbert function value one for every g in the grading monoid G = N/L. In this paper we show that if L is twodimensional, then the toric Hilbert scheme of L is smooth and irreducible. This result is false for lattices of dimension three and higher as the toric Hilbert...

An inequality between the number of coverings in the ordered set J(Con L) of join irreducible congruences on a lattice L and the size of L is given. Using this inequality it is shown that this ordered set can be computed in time O(n 2 log 2 n), where n = jLj. This paper is motivated by the problem of eeciently calculating and representing the congruence lattice Con L of a nite lattice L. Of cou...

In this paper we study the set of prime ideals in vector lattices and how properties structure lattice question. The different that will be considered are firstly, all or none order dense, secondly, there only finitely many ideals, thirdly, every ideal is principal, lastly, ascending chain stationary (a property refer to as Noetherian). We also completely characterize piecewise polynomials, whi...

The toric Hilbert scheme of a lattice L ⊆ Z is the multigraded Hilbert scheme parameterizing all ideals in k[x1, . . . , xn] with Hilbert function value one for every g in the grading monoid G = N/L. In this paper we show that if L is twodimensional, then the toric Hilbert scheme of L is smooth and irreducible. This result is false for lattices of dimension three and higher as the toric Hilbert...

A completion via Frink ideals is used to define a convex powerdomain of an arbitrary continuous lattice as a continuous lattice. The powerdomain operator is a functor in the category of continuous lattices and continuous inf-preserving maps and preserves projective limits and surjectivity of morphisms; hence one can solve domain equations in which it occurs. Analogous results hold for algebraic...