The notions of pre-local function, semi-local functions and α-local functions with respect to a topology and an ideal are introduced, and several properties are investigated. Also, the concept of P -I-open sets and P -I-closed sets in ideal topological spaces are discussed. Relations between I-open sets and P -I-open sets are provided, and several properties related to P -I-open sets, pre-local...

In 1964, Hayashi [8] defined and studied the notions of ?-dense in itself sets and ?-perfect subsets in ideal topological spaces. In 1999, Dontchev et al. [5] have studied the notion of Ideal resolvability through codense and completely codense ideal topological spaces. Recently, in the year 2004, Keskin, Noiri and Yuksel [12] have introduced and studied the concepts of fI -sets and fI -continu...

In this paper, it is proved that every non-zero continuous operator with modulus on an lp-space whose modulus is quasinilpotent at a non-zero positive vector has a non-trivial modulus hyperinvariant closed ideal. AMS Subject Classification: 47A15

Let R be a local, Noetherian ring and I ⊆ R an ideal. A question of Kodiyalam asks whether for fixed i > 0, the polynomial giving the ith Betti number of In has degree equal to the analytic spread of I minus one. Under mild conditions on R, we show that the answer is positive in a number of cases, including when I is divisible by m or I is an integrally closed m-primary ideal.

The set of all m-tuples of compatible full conditional distributions on discrete random variables is an algebraic set whose defining ideal is a unimodular toric ideal. We identify the defining polynomials of these ideals with closed walks on a bipartite graph. Our algebraic characterization provides a natural generalization of the requirement that compatible conditionals have identical odds rat...

The non-commutative analytic Toeplitz algebra is the wot–closed algebra generated by the left regular representation of the free semigroup on n generators. We obtain a distance formula to an arbitrary wotclosed right ideal and thereby show that the quotient is completely isometrically isomorphic to the compression of the algebra to the orthogonal complement of the range of the ideal. This is us...

We characterize the holomorphic mappings f between complex Banach spaces that may be written in the form f = T ◦ g, where g is another holomorphic mapping and T belongs to a closed surjective operator ideal.

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.

In an ideal world, rise and fall times would be infinitely fast and every edge of a digital stream would consistently fall the exact same time away from the last. The end result would be no jitter, no wiggling, and no eyes diagrams that suffer from being closed or close to closed. Unfortunately it is not a perfect world, and what once was conceived as an infinitely fast edge, becomes slower as ...

A BSS machine is δ-uniform if it does not use exact tests; such machines are equivalent (modulo parameters) to Type 2 Turing machines. We define a notion of closure related to Turing machines for archimedean fields, and show that such fields admit nontrivial δ-uniformly decidable sets iff they are not Turing closed. Then, the partially ordered set of Turing closed fields is proved isomorphic to...