相关论文: Groebner bases, initial ideals and initial algebra…
In these self-contained low prerequisite introductory notes we first present (in part 1) basic concepts of set theory and algebra without explicit category theory. We then present (in part 2) basic category theory involving a somewhat…
We introduce binomial edge ideals attached to a simple graph $G$ and study their algebraic properties. We characterize those graphs for which the quadratic generators form a Gr\"obner basis in a lexicographic order induced by a vertex…
We show that high Veronese subrings of any commutative graded ring have a Grobner basis with all relations of degree 2. (The d-th Veronese subring of a ring A_0 + A_1 + A_2 + ... is the ring A_0 + A_d + A_{2d} + ...; ``high'' means we take…
It is known that the initial ideals of generic ideals are the same. Moreno-Soc\'{i}as conjectured that the initial ideal of generic ideals with respect to the degree reverse lexicographic order is weakly reverse lexicographic. In the first…
There are several efficient methods to solve linear interval polynomial systems in the context of interval computations, however, the general case of interval polynomial systems is not yet covered as well. In this paper we introduce a new…
One of the main contributions which Volker Weispfenning made to mathematics is related to Groebner bases theory. In this paper we present an algorithm for computing all algebraic intermediate subfields in a separably generated unirational…
The correspondence found by Faulkner between inner ideals of the Lie algebra of a simple algebraic group and shadows on long root groups of the building associated with the algebraic group is shown to hold in greater generality (in…
In this expository style of writing I will give an introduction of Gr\"{o}bner bases and compute it for some algebras and then show how to use it to compute Hilbert series for algebras from chains.
We give a response to a question posed by Groethendieck on the transfert of the properties: reduced, normal, domain, regular, complete intersection, Gorenstein, Cohen-Macaulay, to the completed tensor product of two Noetherian algebras on a…
We study the ideal structure of $C^*$-algebras arising from $C^*$-correspondences. We prove that gauge-invariant ideals of our $C^*$-algebras are parameterized by certain pairs of ideals of original $C^*$-algebras. We show that our…
We continue the study of r-ideals, l-ideals, and HSA's in operator algebras. Some applications are made to the structure of operator algebras, including Wedderburn type theorems for a class of operator algebras. We also consider the…
We study existence and computability of finite bases for ideals of polynomials over infinitely many variables. In our setting, variables come from a countable logical structure A, and embeddings from A to A act on polynomials by renaming…
We determine all the ideals of the homological Goldman Lie algebra, which reflects the structure of an oriented surface.
We describe the primitive ideal spaces and the Jacobson topologies of a special class of topological graph algebras.
In this paper we present the first-ever computer formalization of the theory of Gr\"obner bases in reduction rings, which is an important theory in computational commutative algebra, in Theorema. Not only the formalization, but also the…
Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.
Starting from classical algebraic geometry over the complex numbers (as it can be found for example in Griffiths and Harris it was the goal of these lectures to introduce some concepts of the modern point of view in algebraic geometry. Of…
In this paper we extend the characterisation of kernels in semirings as subtractive ideals to general algebras. We then analyse the counterparts of ``subtractive'' and ``ideal'' in several different algebraic settings.
We investigate Gr\"obner bases of contraction ideals under some monomial homomorphisms. As an application of our theorem, we generalize the result of Aoki--Hibi--Ohsugi--Takemura and Hibi-Ohsugi. Using our results, one can provide many…
In the context of algebraic statistics an experimental design is described by a set of polynomials called the design ideal. This, in turn, is generated by finite sets of polynomials. Two types of generating sets are mostly used in the…