Related papers: A short note on containment of cores

A cofactor representation of an ideal element, that is, a representation in terms of the generators, can be considered as a certificate for ideal membership. Such a representation is typically not unique, and some can be a lot more…

We show that the following two theories are equiconsistent: (T) ZFC, CH and "There is a dense ideal on the first uncountable cardinal such that if j is the generic embedding associated with it then its restriction on ordinals is independent…

We introduce the general notions of an index and a core of a relation. We postulate a limited form of the axiom of choice -- specifically that all partial equivalence relations have an index -- and explore the consequences of adding the…

We find formulas for the graded core of certain m-primary ideals in a graded ring. In particular, if S is the section ring of an ample line bundle on a Cohen-Macaulay complex projective variety, we show that under suitable hypothesis, the…

We show that every countable ideal of degrees that are low for isomorphism is contained in a principal ideal of degrees that are low for isomorphism by adapting an exact pair construction. We further show that within the hyperimmune-free…

We demonstrate that our model [Phys.Rev. E91, 032312 (2015)] serves as a useful tool to trace the evolution of equilibrium configurations of one-component charged particles confined in a disk. Our approach reduces significantly the…

We show that errors in data transmitted through linear codes can be thought of as codewords of minimum weight of new linear codes. To determine errors we can then use methods specific to finding such special codewords. One of these methods…

We show that if a graded submodule of a Noetherian module cannot be written as a proper intersection of graded submodules, then it cannot be written as a proper intersection of submodules at all. More generally, we show that a natural…

Specific data compression techniques, formalized by the concept of coresets, proved to be powerful for many optimization problems. In fact, while tightly controlling the approximation error, coresets may lead to significant speed up of the…

We evaluate the intrinsic three dimensional shapes of molecular cores, by analysing their projected shapes. We use the recent catalogue of molecular line observations of Jijina et al. and model the data by the method originally devised for…

We investigate the problem of factorization of large numbers on a quantum computer which we imagine to be realized within a linear ion trap. We derive upper bounds on the size of the numbers that can be factorized on such a quantum…

We withdraw our paper as the factorizability of the correlation functions is unproven.

A commutative ring is said to have ITI with respect to an ideal a if the a-torsion functor preserves injectivity of modules. Classes of rings with ITI or without ITI with respect to certain sets of ideals are identified. Behaviour of ITI…

We obtain strong coloring theorems at successors of singular cardinals from failures of certain instances of simultaneous reflection of stationary sets. Along the way, we establish new results in club-guessing and in the general theory of…

The principal result is a primary decomposition of ideals generated by the (2x2)-subpermanents of a generic matrix. These permanental ideals almost always have embedded components and their minimal primes are of three distinct heights. Thus…

Equality of the second order arithmetic means of two principal ideals does not imply equality of their first order arithmetic means (second order equality cancellation). We provide fairly broad sufficient conditions on one of the principal…

In this short note, we show some inequalities on Cartan matrices, centers and socles of blocks of group algebras. Our main theorems are generalizations of the facts on dimension of Reynolds ideals.

The core of an module is the intersection of all its reductions. The main result asserts that the core of a finitely generated, torsion-free, integrally closed module over a two dimensional regular local ring is the product of the module…

In our paper "Essential normality, essential norms and hyperrigidity" we claimed that the restriction of the identity representation of a certain operator system (constructed from a polynomial ideal) has the unique extension property,…

The main result of this paper is that all antichains are finite in the poset of monomial ideals in a polynomial ring, ordered by inclusion. We present several corollaries of this result, both simpler proofs of results already in the…