相关论文: Minimal primes and radicality of ideals generated …
Our focus in this paper is in effective computation of the core core(I) of an ideal I which is defined to be the intersection of all minimal reductions of I. The first main result is a closed formula for the graded core(m) of the maximal…
In this article we prove that for a large class of 2-dimensional minimal cones (including almost all 2-dimensional minimal cones that we know), the almost orthogonal union of any two of them is still a minimal cone. Comparing to existing…
The structure of zero and nonzero minors in the Grassmannian leads to rich combinatorics of matroids. In this paper, we investigate an even richer structure of possible equalities and inequalities between the minors in the positive…
The Dixmier-Moeglin Equivalence (for short, the DM-equivalence) is the equivalence of three distinguishing properties of prime ideals in a non-commutative algebra A. These properties are of (i) being primitive, (ii) being rational, and…
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…
Recent results of Kahle and Miller give a method of constructing primary decompositions of binomial ideals by first constructing "mesoprimary decompositions" determined by their underlying monoid congruences. Monoid congruences (and…
We consider the fiber cone of monomial ideals. It is shown that for monomial ideals $I\subset K[x,y]$ of height $2$, generated by $3$ elements, the fiber cone $F(I)$ of $I$ is a hypersurface ring, and that $F(I)$ has positive depth for…
Let $R$ be a normal Noetherian local domain of Krull dimension two. We examine intersections of rank one discrete valuation rings that birationally dominate $R$. We restrict to the class of prime divisors that dominate $R$ and show that if…
We study the ideals of the partition, Brauer, and Jones monoid, establishing various combinatorial results on generating sets and idempotent generating sets via an analysis of their Graham--Houghton graphs. We show that each proper ideal of…
We consider the problem of minimizing convex combinations of the first two eigenvalues of the Dirichlet-Laplacian among open sets of $R^N$ of fixed measure. We show that, by purely elementary arguments, based on the minimality condition, it…
D. Rees and J. Sally defined the core of an $R$-ideal $I$ as the intersection of all $($minimal$)$ reductions of $I$. However, it is not easy to give an explicit characterization of it in terms of data attached to the ideal. Until recently,…
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…
In commutative ring theory, there is a theorem of Cohen which states that if in a commutative ring all prime ideals are finitely generated then every ideal is finitely generated. However, it is known that having only maximal ideals finitely…
We investigate the structure of ideals generated by binomials (polynomials with at most two terms) and the schemes and varieties associated to them. The class of binomial ideals contains many classical examples from algebraic geometry, and…
Radical binomial ideals associated with finite lattices are studied. Gr\"obner basis theory turns out to be an efficient tool in this investigation.
In this paper we introduce prime fuzzy ideals over a noncommutative ring. This notion of primeness is equivalent to level cuts being crisp prime ideals. It also generalizes the one provided by Kumbhojkar and Bapat in [Not-so-fuzzy fuzzy…
We study minimal reductions of edge ideals of graphs and determine restrictions on the coefficients of the generators of these minimal reductions. We prove that when $I$ is not basic, then $\core{I}\subset \m I$, where $I$ is an edge ideal…
This paper presents a unified framework for determining the congruences on a number of monoids and categories of transformations, diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative…
When anti-canonical rings are finitely generated, we give a characterization of adjoint ideals using ultra-Frobenii, a characteristic zero analogue of Frobenius morphisms. This characterization enables us to give an alternative proof of a…
Let M be a fixed left R-module. For a left R-module X, we introduce the notion of M-prime (resp. M-semiprime) submodule of X such that in the case M=R, which coincides with prime (resp. semiprime) submodule of X. Other concepts encountered…