In this paper, we introduce and study the stable topology on the set of prime filters of a bounded 0-distributive lattice. The stable topology is a subtopology of the hull kernel topology on the set of prime filters of a bounded 0-distributive lattice. Sufficient condition is given under which the hull kernel topology and stable topology coincide on the set of prime filters (the set of maximal ...

We introduce the notion of (maximal) multi-truncations on a vector lattice as generalization truncations, an object recent origin. obtain Johnson–Kist type representation lattices with maximal almost-finite extended-real continuous functions. The spectrum that allows such is particular set prime ideals equipped Hull–Kernel topology. Various representations from existing literature will appear s...

in this paper the family of elliptic curves over q given by the equation ep :y2 = (x - p)3 + x3 + (x + p)3 where p is a prime number, is studied. itis shown that the maximal rank of the elliptic curves is at most 3 and someconditions under which we have rank(ep(q)) = 0 or rank(ep(q)) = 1 orrank(ep(q))≥2 are given.

Let R be a commutative integral domain with quotient field K and let P be a nonzero strongly prime ideal of R. We give several characterizations of such ideals. It is shown that (P : P) is a valuation domain with the unique maximal ideal P. We also study when P^{&minus1} is a ring. In fact, it is proved that P^{&minus1} = (P : P) if and only if P is not invertible. Furthermore, if P is invertib...

The maximal prime decomposition (MPD) of a Bayesian network is a hierarchical structure, which represents conditional independency information. The MPD representation has shown to facilitate probabilistic inference in uncertainty management. One method for building the MPD involves applying the moralization and triangulation procedures to the given Bayesian network. An alternative method constr...

We study a two-dimensional discrete directional maximal operator along the set of the prime numbers. show existence vectors, which are lattice points in a sufficiently large annulus, for $\ell^2$ norm associated maximal operator, with supremum taken over all scales, grows an epsilon power number vectors. This paper is follow-up to prior work on directional integers by first and third author.

We consider properties of residuated lattices with universal quantifier and show that, for a residuated lattice $X$, $(X, forall)$ is a residuated lattice with a quantifier if and only if there is an $m$-relatively complete substructure of $X$. We also show that, for a strong residuated lattice $X$, $bigcap {P_{lambda} ,|,P_{lambda} {rm is an} m{rm -filter} } = {1}$ and hence that any strong re...

Reduced products are generalizations of ultraproducts where the filter used need not be an ultrafilter. With a suitable choice of filter, we can then get a more constructive model of non-standard analysis. We study properties of such reduced products and investigate what classical results are still valid in a constructive setting. A boundedness principle BD, not derivable in pure constructive m...