Instance retraction is a difficult problem for concept learning by version spaces. In this paper, two new version-space representations are introduced: instance-based maximal boundary sets and instancebased minimal boundary sets. They are correct representations for the class of admissible concept languages and are efficiently computable. Compared to other representations, they are the most eff...

Let H∞(D) denote the algebra of bounded analytic functions on the open unit disc in the complex plane. For a function g ∈ L∞(D), the Hankel-type operator Sg is defined by Sg(f) = gf +H∞(D). We give here an overview of the study of the symbol of the Hankel-type operator, with emphasis on those symbols for which the operator is compact, weakly compact, or completely continuous. We conclude with a...

We give conditions for a maximal divisorial ideal to be t-maximal and show with examples that, even in a completely integrally closed domain, maximal divisorial ideals need not be t-maximal.

It is shown that every dp-minimal integral domain R a local ring and for non-maximal prime ideal ℘ of R, the localization R℘ valuation ℘R℘ = ℘. Furthermore, if only its residue field infinite or finite maximal principal.

In this work, we attempt to investigate the connection between various types of ideals (for examples (m,n)-ideal, bi-ideal, interior-ideal, quasi-ideal, prime-ideal and maximal-ideal) of an ordered semigroup (S, ·,≤) and the corresponding, hyperideals of its EL-hyperstructure (S, ∗) (if exists). Moreover, we construct the class of EL-Γ-semihypergroup, associated to a partially-ordered Γsemigroup.

Suppose M is a maximal ideal of a commutative integral domain R and that some power Mn of M is finitely generated. We show that M is finitely generated in each of the following cases: (i) M is of height one, (ii) R is integrally closed and htM = 2, (iii) R = K[X; S̃] is a monoid domain over a field K, where S̃ = S ∪ {0} is a cancellative torsion-free monoid such that ⋂∞ m=1 mS = ∅, and M is the m...

Let ω1 be the rst uncountable ordinal. A result of Rudin implies that bounded operators on the Banach space C([0, ω1]) of continuous functions on the ordinal interval [0, ω1] have a natural representation as [0, ω1]× [0, ω1]-matrices. Loy and Willis observed that the set of operators whose nal column is continuous when viewed as a scalar-valued function on [0, ω1] de nes a maximal ideal of codi...

Introduction. L. Fuchs [2 ] has given for Noetherian rings a theory of the representation of an ideal as an intersection of primal ideals, the theory being in many ways analogous to the classical Noether theory. An ideal Q is primal if the elements not prime to Q form an ideal, necessarily prime, called the adjoint of Q. Primary ideals are necessarily primal, but not conversely. Analogous resul...