Related papers: Rees algebra and almost linearly presented ideals …
A mistake concerning the ultra \textit{LI}-ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an \textit{LI}-ideal to be an ultra \textit{LI}-ideal are given. Moreover, the notion of…
This work is about symbolic powers of codimension two perfect ideals in a standard polynomial ring over a field, where the entries of the corresponding presentation matrix are general linear forms. The main contribution of the present…
In this paper, we study the $F$-rationality of the Rees algebra and the extended Rees algebra of $\mathfrak{m}$-primary ideals in excellent local rings $(R, \mathfrak{m})$ of prime characteristic. We partially answer some conjectures and…
We compute a minimal bigraded resolution of the Rees Algebra associated to a proper rational parametrization of a monomial plane curve. We describe explicitly both the bigraded Betti numbers and the maps of the resolution in terms of a…
A model of representations of a Lie algebra is a representation which a direct sum of all irreducible finite dimensional representations taken with multiplicity $1$. In the paper an explicit construction of a model of representation for all…
We study the meet irreducible ideals in certain direct limit algebras, namely the strongly maximal triangular subalgebras of AF C*-algebras. These ideals have a description in terms of the coordinates, or spectrum, that is a natural…
For any finitely generated abelian group $Q$, we reduce the problem of classification of $Q$-graded simple Lie algebras over an algebraically closed field of "good" characteristic to the problem of classification of gradings on simple Lie…
We study the question of finite generation of saturated multi-Rees algebras and investigate the asymptotic behaviour of related length functions. In the setup of excellent local domains, we show that the saturated multi-Rees algebra of a…
In this work, we extend the definition of the graded prime ideals from those in commutative graded rings to the ideals over graded Lie algebras. We prove some facts about graded prime Lie ideals in arbitrary Lie algebras that are similar to…
In this paper we continue the study of the subalgebra lattice of a Leibniz algebra. In particular, we find out that solvable Leibniz algebras with an upper semi-modular lattice are either almost-abelian or have an abelian ideal spanned by…
Let $E$ be a module of projective dimension one over a Noetherian ring $R$ and consider its Rees algebra $\mathcal{R}(E)$. We study this ring as a quotient of the symmetric algebra $\mathcal{S}(E)$ and consider the ideal $\mathcal{A}$…
The supremum of reduction numbers of ideals having principal reductions is expressed in terms of the integral degree, a new invariant of the ring, which is finite provided the ring has finite integral closure. As a consequence, one obtains…
We classify all graphs for which the Rees algebras of their edge ideals are normal and have regularity equal to their matching numbers.
Using a new powerful technique based on the notion of megaideal, we construct a complete set of inequivalent realizations of real Lie algebras of dimension no greater than four in vector fields on a space of an arbitrary (finite) number of…
Let W be an associative PI algebra over a field F of characteristic zero, graded by a finite group G. Let id_{G}(W) denote the T-ideal of G-graded identities of W. We prove: 1. {[G-graded PI equivalence]} There exists a field extension K of…
Leibniz algebras are non-antisymmetric generalizations of Lie algebras that have attracted substantial interest due to their close relation with the latter class. A Leibniz algebra $A$ is called perfect if it coincides with its derived…
The Qth-power algorithm for computing structured global presentations of integral closures of affine domains over finite fields is modified to compute structured presentations of integral closures of ideals in affine domains over finite…
The Lefschetz question asks if multiplication by a power of a general linear form, $L$, on a graded algebra has maximal rank (in every degree). We consider a quotient by an ideal that is generated by powers of linear forms. Then the…
We characterize ideals whose adjoints are determined by their Rees valuations. We generalize the notion of a regular system of parameters, and prove that for ideals generated by monomials in such elements, the integral closure and adjoints…
We consider a class of algebraic dynamical systems introduced by Kitchens and Schmidt. Under a weak finiteness condition -- the Descending Chain Condition -- the dual modules have finite presentations. Using methods from commutative algebra…