Related papers: Indecomposable Ideals in Incidence Algebras

Let $SP$ be the set of upper strongly porous at $0$ subsets of $\mathbb R^{+}$ and let $\hat I(SP)$ be the intersection of maximal ideals $I \subseteq SP$. Some characteristic properties of sets $E\in\hat I(SP)$ are obtained. It is shown…

A chopped ideal is obtained from a homogeneous ideal by considering only the generators of a fixed degree. We investigate cases in which the chopped ideal defines the same finite set of points as the original one-dimensional ideal. The…

Regarding non-unique factorization of integer-valued polynomials over a discrete valuation domain $(R,M)$ with finite residue field, it is known that there exist absolutely irreducible elements, that is, irreducible elements all of whose…

We study the algebraic exceptional set for surfaces (S,B) of log general type, when B has at least three irreducible components; we prove that in most cases it is finite or empty.

Let K be a finite field and let X be a subset of a projective space, over the field K, which is parameterized by monomials arising from the edges of a clutter. We show some estimates for the degree-complexity, with respect to the revlex…

Primary decomposition of commutative monoid congruences is insensitive to certain features of primary decomposition in commutative rings. These features are captured by the more refined theory of mesoprimary decomposition of congruences,…

In the same way decomposition spaces, also known as unital 2-Segal spaces, have incidence (co)algebras, and certain relative decomposition spaces have incidence (co)modules, we identify the structures that have incidence bi(co)modules: they…

We consider point sets in the affine plane $\mathbb{F}_q^2$ where each Euclidean distance of two points is an element of $\mathbb{F}_q$. These sets are called integral point sets and were originally defined in $m$-dimensional Euclidean…

A set is introreducible if it can be computed by every infinite subset of itself. Such a set can be thought of as coding information very robustly. We investigate introreducible sets and related notions. Our two main results are that the…

In this paper we describe three different variations of prime ideals: strongly irreducible ideals, strongly prime ideals and insulated prime ideals in the context of Leavitt path algebras. We give necessary and sufficient conditions under…

In this paper, a class of indecomposable positive finite rank elementary operators of order $(n,n)$ are constructed. This allows us to give a simple necessary and sufficient criterion for separability of pure states in bipartite systems of…

We prove that partially ordered set has finite number of finite-dimensional indecomposable nonequivalent Hilbert representations with orthoscalarity condition if and anly if it has finite number of indecomposable linear representations. We…

A tree T is invertible if and only if T has a perfect matching. Godsil considers an invertible tree T and finds that the inverse of the adjacency matrix of T has entries in {0, 1, -1} and is the signed adjacency matrix of a graph which…

All subalgebras, idempotents, left(right) ideals and left quasi-units of two-dimensional algebras are described. Classification of algebras with given number of subalgebras, left(right) ideals are provided. In particular, a list of…

We classify all unmixed monomial ideals I of codimension 2 which are generically a complete intersection and which have the property that the symbolic power algebra A(I) is standard graded. We give a lower bound for the highest degree of a…

Let $G$ be a finite group. The bipartite divisor graph for the set of irreducible complex character degrees is the undirected graph with vertex set consisting of the prime numbers dividing some character degree and of the non-identity…

We say that an inclusion of an algebra $A$ into a $C^*$-algebra $B$ has the ideal separation property if closed ideals in $B$ can be recovered by their intersection with $A$. Such inclusions have attractive properties from the point of view…

A poset is said to be (2+2)-free if it does not contain an induced subposet that is isomorphic to 2+2, the union of two disjoint 2-element chains. Two elements in a poset are indistinguishable if they have the same strict up-set and the…

Given any polynomial $p$ in $C[X]$, we show that the set of irreducible matrices satisfying $p(A)=0$ is finite. In the specific case $p(X)=X^2-nX$, we count the number of irreducible matrices in this set and analyze the arising sequences…

A distributive lattice $L$ with minimum element $0$ is called decomposable if $a$ and $b$ are not comparable elements in $L$ then there exist $\overline{a},\overline{b}\in L$ such that $a=\overline{a}\vee(a\wedge b),…