Related papers: Subideals of operators
Binomial ideals are special polynomial ideals with many algorithmically and theoretically nice properties. We discuss the problem of deciding if a given polynomial ideal is binomial. While the methods are general, our main motivation and…
Trusses, defined as sets with a suitable ternary and a binary operations, connected by the distributive laws, are studied from a ring and module theory point of view. The notions of ideals and paragons in trusses are introduced and several…
We say that an ideal I is homogeneous, if its restriction to any I-positive subset is isomorphic to I. The paper investigates basic properties of this notion -- we give examples of homogeneous ideals and present some applications to…
We continue the study of r-ideals, l-ideals, and HSA's in operator algebras. Some applications are made to the structure of operator algebras, including Wedderburn type theorems for a class of operator algebras. We also consider the…
Let $\b$ be a Borel subalgebra of a simple Lie algebra $\g$ and let $\Ab$ denote the set of all Abelian ideals of $\b$. We consider $\Ab$ as poset with respect to inclusion, the zero ideal being the unique minimal element of $\Ab$. It was…
For commutative rings with identity, we introduce and study the concept of semi $r$-ideals which is a kind of generalization of both $r$-ideals and semiprime ideals. A proper ideal $I$ of a commutative ring $R$ is called semi $r$-ideal if…
The machine learning of lattice operators has three possible bottlenecks. From a statistical standpoint, it is necessary to design a constrained class of operators based on prior information with low bias, and low complexity relative to the…
In this paper, we draw connections between ideal lattices and multivariate polynomial rings over integers using Gr\"obner bases. Ideal lattices are ideals in the residue class ring, $\mathbb{Z}[x]/\langle f \rangle$ (here $f$ is a monic…
We explicitly compute the Hodge ideals of Q-divisors in terms of the V-filtration induced by a local defining equation, inspired by a result of Saito in the reduced case. We deduce basic properties of Hodge ideals in this generality, and…
Neural ideals, originally defined in arXiv:1212.4201, give a way of translating information about the firing pattern of a set of neurons into a pseudomonomial ideal in a polynomial ring. We give a simple criterion for determining whether a…
In this paper, we draw a connection between ideal lattices and Gr\"{o}bner bases in the multivariate polynomial rings over integers. We study extension of ideal lattices in $\mathbb{Z}[x]/\langle f \rangle$ (Lyubashevsky \& Micciancio,…
We consider the set of all the ideals of a ring, endowed with the coarse lower topology. The aim of this paper is to study the topological properties of distinguished subspaces of this space and detect the spectrality of some of them.
In this paper we completely characterize lattice ideals that are complete intersections or equivalently complete intersections finitely generated semigroups of $\bz^n\oplus T$ with no invertible elements, where $T$ is a finite abelian…
In this paper we characterize hemirings in which all $h$-ideals or all fuzzy $h$-ideals are idempotent. It is proved, among other results, that every $h$-ideal of a hemiring $R$ is idempotent if and only if the lattice of fuzzy $h$-ideals…
A subspace H of a Leibniz algebra L is called a quasi-ideal if [H;K] + [K;H] \subseteq H + K for every subspace K of L. They include ideals and subalgebras of codimension one in L. Quasi-ideals of Lie algebras were classified in two…
An ordered semiring is a commutative semiring equipped with a compatible preorder. Ordered semirings generalise both distributive lattices and commutative rings, and provide a convenient framework to unify certain aspects of lattice theory…
We introduce a similarity relation between submodules of a module $M$ over a ring $R$, extending the classical notion of similarity for right ideals. Focusing on (faithfully) projective modules, we establish a sharp lower bound for the…
In this paper, we introduce a new generalization of weakly prime ideals called $I$-prime. Suppose $R$ is a commutative ring with identity and $I$ a fixed ideal of $R$. A proper ideal $P$ of $R$ is $I$-prime if for $a, b \in R$ with $ab \in…
Given an infinite set \Lambda of characters on a compact abelian group we show that \Lambda is a \Lambda(p)-set for all p>2 if and only if the limit order of the ideal of all \Lambda-summing operators coincides with that of the ideal of all…
We provide a correspondence between one-sided coideal subrings and one-sided ideal two-sided coideals in an arbitrary bialgebroid. We prove that, under some expected additional conditions, this correspondence becomes bijective for Hopf…