相关论文: Atoms in Quasilocal Integral Domains

We give examples of atomic integral domains satisfying each of the eight logically possible combinations of existence or non-existence of the following kinds of elements: 1) primes, 2) absolutely irreducible elements that are not prime, and…

In algebra, atomicity is the study of divisibility by and factorizations into atoms (also called irreducibles). In one side of the spectrum of atomicity we find the antimatter algebraic structures, inside which there are no atoms and,…

A semidomain is an additive submonoid of an integral domain that is closed under multiplication and contains the identity element. Although atomicity and divisibility in integral domains have been systematically investigated for more than…

For an integral domain $R$ and a commutative cancellative monoid $M$, the ring consisting of all polynomial expressions with coefficients in $R$ and exponents in $M$ is called the monoid ring of $M$ over $R$. An integral domain is called…

In classical factorization theory, an integral domain is called \emph{atomic} if every nonzero nonunit element can be written as a finite product of irreducible elements. Here, we introduce and study a weaker notion of atomicity, which…

Let A be an associative algebra with identity over a field k. An atomistic subsemiring R of the lattice of subspaces of A, endowed with the natural product, is a subsemiring which is a closed atomistic sublattice. When R has no zero…

A commutative monoid is atomic if every non-invertible element factors into irreducibles (also called atoms), while an integral (semi)domain is atomic if its multiplicative monoid is atomic. Notions weaker than atomicity have been…

Let $K$ be a number field with ring of integers $\mathbb{Z}_K$. We prove two asymptotic formulas connected with the distribution of irreducible elements in $\mathbb{Z}_K$. First, we estimate the maximum number of nonassociated irreducibles…

Quantum embedding theories are promising approaches to investigate strongly-correlated electronic states of active regions of large-scale molecular or condensed systems. Notable examples are spin defects in semiconductors and insulators. We…

An integral domain is atomic if every nonzero nonunit factors into irreducibles. Let $R$ be an integral domain. We say that $R$ is a bounded factorization domain if it is atomic and for every nonzero nonunit $x \in R$, there is a positive…

In general, ring theory is focused on atomic rings, i.e. rings in which every element has some factorization into irreducible elements. In a recent paper of Boynton and Coykendall \cite{BC}, the two authors introduce two properties that are…

Is quantum mechanics (QM) local or nonlocal? Different formulations/interpretations (FI) of QM, with or without hidden variables, suggest different answers. Different FI's can be viewed as different algorithms, which leads us to propose an…

Quasiminimal sets are sets for which a pertubation can decrease the area but only in a controlled manner. We prove that in dimensions $2$ and $3$, such sets separate a locally finite family of local John domains. Reciprocally, we show that…

We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…

A CP semigroup is a semigroup of normal unit-preserving completely positive maps acting on the algebra B(H) of all operators on a separable Hilbert space H. Such a semigroup has a natural generator L; since the individual maps of the…

Quasi-set theory allows us a non trivial relation between indistinguishability and nonlocality into the context of Einstein- Podolsky-Rosen experiment. Quasi-set theory is a set theory which provides a manner for dealing with collections of…

An integral domain $R$ is called atomic if every nonzero nonunit of $R$ factors into irreducibles, while $R$ satisfies the ascending chain condition on principal ideals if every ascending chain of principal ideals of $R$ stabilizes. It is…

A numerical semigroup $S$ is a cofinite, additively-closed subset of the nonnegative integers that contains $0$. In this paper, we initiate the study of atomic density, an asymptotic measure of the proportion of irreducible elements in a…

In this paper, we address various aspects of divisibility by irreducibles in rings consisting of integer-valued polynomials. An integral domain is called atomic if every nonzero nonunit factors into irreducibles. Atomic domains that do not…

We review recent progress in understanding the notion of locality in integrable quantum lattice systems. The central concept are the so-called quasilocal conserved quantities, which go beyond the standard perception of locality. Two…