Related papers: Principal ideals in a plactic monoid always inters…
Motivated by recent work with Mazorchuk, we characterize the conditions under which the intersection of two principal order ideals in the Bruhat order is boolean. That characterization is presented in three versions: in terms of reduced…
We study two partial orders on $[x_1,...,x_n]$, the free abelian monoid on ${x_1,...,x_n}$. These partial orders, which we call the ``strongly stable'' and the ``stable'' partial order, are defined by the property that their filters are…
In the first chapter we present new results related on monomial ideals of Borel type. Also, we introduce a new class of monomial ideals, called $\de$-fixed ideals, which generalize the class of $p$-Borel ideals and we extend several results…
The associated prime ideals of powers of polymatroidal ideals are studied, including the stable set of associated prime ideals of this class of ideals. It is shown that polymatroidal ideals have the persistence property and for transversal…
In this paper, we provide a complete description of the minimal primes of ideals generated by adjacent $2$-minors, in terms of the so-called admissible sets and associated lattice ideals. We prove that for these ideals, the properties of…
Ideals are one of the main topics of interest to the study of the order structure of an algebra. Due to their nice properties, ideals have an important role both in lattice theory and semigroup theory. Two natural concepts of ideal can be…
Squarefree monomial ideals arising from finite meet-semilattices and their free resolutions are studied. For the squarefree monomial ideals corresponding to poset ideals in a distributive lattice the Alexander dual is computed.
We consider rings whose one-sided ideals are close to automorphism-invariant modules. We study rings in which every (finitely generated) right ideal is automorphism invariant and rings in which every right ideal is a finite direct sum of…
We introduce a class of Stanley-Reisner ideals called generalized complete intersection, which is characterized by the property that all the residue class rings of powers of the ideal have FLC. We also give a combinatorial characterization…
The properties of the intersection algebra of two principal monomial ideals in a polynomial ring are investigated in detail. Results are obtained regarding the Hilbert series and the canonical ideal of the intersection algebra using methods…
The generic link of an unmixed radical ideal is radical (in fact, prime). We show that the squarefreeness of the initial ideal and $F$-purity are, however, not preserved along generic links. On the flip side, for several important cases in…
We will study the presentations of fundamental groups of the complement of complexified real affine line arrangements that do not contain two parallel lines. By Yoshinaga's minimal presentation, we can give positive homogeneous…
We introduce a monomial ideal whose standard monomials encode the vertices of all fibers of a lattice. We study the minimal generators, the radical, the associated primes and the primary decomposition of this ideal, as well as its relation…
The two main approaches to the study of irreducible representations of orders (via traces and Poisson orders) have so far been applied in a completely independent fashion. We define and study a natural compatibility relation between the two…
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…
Ideals in infinite-dimensional polynomial rings that are invariant under the action of the monoid of increasing functions have been extensively studied recently. Of particular interest is the asymptotic behavior of truncations of such an…
We show that every automorphism of a thick twin building interchanging the halves of the building maps some residue to an opposite one. Furthermore we show that no automorphism of a locally finite 2-spherical twin building of rank at least…
It is shown that every Leavitt path algebra L of an arbitrary directed graph E over a field K is an arithmetical ring, that is, the two-sided ideals of L form a distributive lattice. It is also shown that L is a multiplication ring, that…
A variety is finitely universal if its lattice of subvarieties contains an isomorphic copy of every finite lattice. Examples of finitely universal varieties of semigroups have been available since the early 1970s, but it is unknown if there…
A monoid $S$ is right coherent if every finitely generated subact of every finitely presented right $S$-act is finitely presented. The corresponding notion for a ring $R$ states that every finitely generated submodule of every finitely…