Prelinear Hilbert algebras

Representation of Prelinear Residuated Algebras

In 1998, Hájek established a representation theorem of BL-algebrs as all subdirect products of linear BL-algebrs. We establish a similar result for the much wider class of prelinear residuated algebras, in which neither the lattice structure nor the divisibility of the monoid operation is assumed. We show, in the case of prelinear residuated lattices, that this order embedding becomes a lattice...

Hilbert Algebras of Fractions

Hilbert modules over pro-C*-algebras

In this paper, we generalize some results from Hilbert C*-modules to pro-C*-algebra case. We also give a new proof of the known result that l2(A) is aHilbert module over a pro-C*-algebra A.

APPLICATIONS OF SOFT SETS IN HILBERT ALGEBRAS

The concept of soft sets, introduced by Molodtsov [20] is a mathematicaltool for dealing with uncertainties, that is free from the difficultiesthat have troubled the traditional theoretical approaches. In this paper, weapply the notion of the soft sets of Molodtsov to the theory of Hilbert algebras.The notion of soft Hilbert (abysmal and deductive) algebras, soft subalgebras,soft abysms and sof...

Hilbert Functions of Veronese Algebras

We study the Hilbert polynomials of non-standard graded algebras R, that are finitely generated on generators not all of degree one. Given an expression P (R, t) = a(t)/(1 − t) for the Poincaré series of R as a rational function, we study for 0 ≤ i ≤ l the graded subspaces ⊕kRkl+i (which we denote R[l; i]) of R, in particular their Poincaré series and Hilbert functions. For example, we prove th...