相关论文: On the symmetric and Rees algebras of certain dete…

In this article we show that the symbolic Rees algebra of a mixed ladder determinantal ideal is strongly $F$-regular. Furthermore, we prove that the symbolic associated graded algebra of a mixed ladder determinantal ideal is $F$-pure. The…

We prove that semialgebraic sets of rectangular matrices of a fixed rank, of skew-symmetric matrices of a fixed rank and of real symmetric matrices whose eigenvalues have prescribed multiplicities are minimal submanifolds of the space of…

Algebraic dichotomy is a generalization of an exponential dichotomy (Lin, JDE2009). This paper gives a version of Hartman-Grobman linearization theorem assuming that linear system admits an algebraic dichotomy, which generalizes the…

We provide a sufficient condition for a polynomial ring, not necessarily commutative, to have a first-order definition for the rational integers.

This paper explores the relation between multi-Rees algebras and ideals that arise in the study of toric dynamical systems from the theory of chemical reaction networks.

This is the first installment of an exposition of an ACL2 formalization of elementary linear algebra, focusing on aspects of the subject that apply to matrices over an arbitrary commutative ring with identity, in anticipation of a future…

Let $R= S/I$ where $S=k[T_1, \ldots, T_n]$ and $I$ is a homogeneous ideal in $S$. The acyclic closure $R \langle Y \rangle $ of $k$ over $R$ is a DG algebra resolution obtained by means of Tate's process of adjoining variables to kill…

Let $R=k[x,y,z]$ be a standard graded $3$-variable polynomial ring, where $k$ denotes any field. We study grade $3$ homogeneous ideals $I \subseteq R$ defining compressed rings with socle $k(-s)^{\ell} \oplus k(-2s+1)$, where $s \geq3$ and…

Let $R=\k[x,y,z]$ and $I=(f_0,\dots,f_{n-1})$ be a height two perfect ideal which is almost linearly presented (that is, all but the last column have linear entries, but the last column has entries which are homogeneous of degree $2$).…

In this paper, we prove a theorem on the distribution of primes in cubic progressions on average.

Extending the notion of indispensable binomials of a toric ideal, we define indispensable monomials of a toric ideal and establish some of their properties. They are useful for searching indispensable binomials of a toric ideal and for…

Let K be a number field, and L be a finite normal extension of K with Galois group G. It is known that the number of Frobenius automorphisms corresponding to prime ideals, whose norms are less than x, is equivalent to the logarithmic…

We classify all graphs for which the Rees algebras of their edge ideals are normal and have regularity equal to their matching numbers.

In the present work, a procedure for determining idempotents of a commutative ring having a sequence of ideals with certain properties is presented. As an application of this procedure, idempotent elements of various commutative rings are…

We give a new elementary proof of Landau's Prime Ideal Theorem. The proof is an extension of Richter's proof of the Prime Number Theorem. The main result contains other results related to the equidistribution of the prime ideal counting…

We make progress towards characterizing the algebraic matroid of the determinantal variety defined by the minors of fixed size of a matrix of variables. Our main result is a novel family of base sets of the matroid, which characterizes the…

Our purpose is to study the cohomological properties of the Rees algebras of a class of ideals generated by quadrics. For all such ideals $I\subset R = K[x,y,z]$ we give the precise value of depth $R[It]$ and decide whether the…

In this expositional paper, we discuss commutative algebra -- a study inspired by the properties of integers, rational numbers, and real numbers. In particular, we investigate rings and ideals, and their various properties. After, we…

The main purpose of this paper is to investigate prime, primary, and maximal ideals of semirings. The localization and primary decomposition of ideals in semirings are also studied.

Ideals in the ring of power series in three variables can be classified based on algebra structures on their minimal free resolutions. The classification is incomplete in the sense that it remains open which algebra structures actually…