The main theorems of this paper give sharp upper bounds for the minimum distances of one-sided ideals in structural matrix rings defined by directed graphs. It is very well known that additional algebraic structure can give advantages for coding applications (see, for example, [8]). Serious attention in the literature has been devoted to considering properties of ideals in various ring construc...

The space of unitary local systems of rank one on the complement of an arbitrary divisor in a complex projective algebraic variety can be described in terms of parabolic line bundles. This space is a natural setting for studying global invariants of singularities involving multiplier ideals. We show that multiplier ideals provide natural stratifications of this space. We prove a structure theor...

Convex-concave sets and Arnold hypothesis. The notion of convexity is usually defined for subsets of affine spaces, but it can be generalized for subsets of projective spaces. Namely, a subset of a projective space RP is called convex if it doesn’t intersect some hyperplane L ⊂ RP and is convex in the affine space RP \L. In the very definition of the convex subset of a projective space appears ...

In this study, we present generalizations of the concept r-ideals in commutative rings with a nonzero identity. Let R be ring 0 ≠ 1 and L(R) lattice all ideals R. Suppose that ϕ:L(R) → ∪ {Ø} is function. A proper ideal I called ϕ-r-ideal if whenever ab ∈ Ann(a) = (0) imply b for each a,b addition to proven many properties ϕ-r-ideals, also examine ϕ-r-ideals trivial extension use them characteri...

The space of unitary local systems of rank one on the complement of an arbitrary divisor in a complex projective algebraic variety can be described in terms of parabolic line bundles. This space is a natural setting for studying global invariants of singularities involving multiplier ideals. We show that multiplier ideals provide natural stratifications of this space. We prove a structure theor...

We develop general techniques and present an approach to solve the problem of constructing a maximal Banach ideal (A,A) which does not satisfy a transfer of the norm estimation in the principle of local reflexivity to its norm A. This approach leads us to the investigation of product operator ideals containing L2 (the collection of all Hilbertian operators) as a factor. Using the local properti...