Related papers: Semigroup Graded Stillman's Conjecture

The purpose of this paper is to prove that certain limits of polynomial rings are themselves polynomial rings, and show how this observation can be used to deduce some interesting results in commutative algebra. In particular, we give two…

Let $\mathbf{A}_{n, m}$ be the polynomial ring $\text{Sym}(\mathbf{C}^n \otimes \mathbf{C}^m)$ with the natural action of $\mathbf{GL}_m(\mathbf{C})$. We construct a family of $\mathbf{GL}_m(\mathbf{C})$-stable ideals $J_{n, m}$ in…

In 2016 Ananyan and Hochster proved Stillman's conjecture by showing the existence of a uniform upper bound on the length of an $R_\eta$-sequence containing fixed $n$ forms of degree at most $d$ in polynomial rings over a field. This result…

In this paper, we will prove some sufficient conditions for the solvability of groups.

We investigate whether the group algebra of a finite group over a localisation of the integers is semiperfect. The main result is a necessary and sufficient arithmetic criterion in the ordinary case. In the modular case, we propose a…

We present two criteria for a group $G$ to satisfy the following statements: any $G$-graded gr-prime (gr-semiprime) right gr-Goldie ring admits a gr-semisimple graded right classical quotient ring. The criterion for gr-semiprime rings is…

We prove an analogue of the celebrated Hall-Higman theorem, which gives a lower bound for the degree of the minimal polynomial of any semisimple element of prime power order $p^{a}$ of a finite classical group in any nontrivial irreducible…

In this paper, we investigate primeness of groupoid graded rings. We provide a set of necessary and sufficient conditions for primeness of a nearly-epsilon strongly groupoid graded ring. Furthermore, we apply our main result to get a…

In this article, we give a complete characterization of semigroup graded rings which are graded von Neumann regular. We also demonstrate our results by applying them to several classes of examples, including matrix rings and groupoid graded…

We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We…

In 2016 Ananyan and Hochster proved Stillman's conjecture by showing the existence of a uniform upper bound for the projective dimension of all homogeneous ideals, in polynomial rings over a field, generated by n forms of degree at most d.…

This paper studies the class group of graded integral domains. As an application, we state a decomposition theorem for class groups of semigroup rings. This recovers well-known results developed for the classic contexts of polynomial rings…

Harm Derksen made a conjecture concerning degree bounds for the syzygies of rings of polynomial invariants in the non-modular case. We provide counterexamples to this conjecture, but also prove a slightly weakened version. We also prove…

We prove an asymptotically tight bound (asymptotic with respect to the number of polynomials for fixed degrees and number of variables) on the number of semi-algebraically connected components of the realizations of all realizable sign…

We give a conditional proof of the Uniform Boundedness Conjecture of Morton and Silverman in the case of polynomials over number fields, assuming a standard conjecture in arithmetic geometry. Our technique simultaneously yields a dynamical…

We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context.…

A generalized numerical semigroup is a submonoid of $\mathbb{N}^d$ with finite complement in it. In this work we study some properties of three different classes of generalized numerical semigroups. In particular, we prove that the first…

Combining recent results on noetherianity of twisted commutative algebras by Draisma and the resolution of Stillman's conjecture by Ananyan-Hochster, we prove a broad generalization of Stillman's conjecture. Our theorem yields an array of…

In this paper, by studying the famous theorem of Pang and Zalcman, we find a normal family and obtain a result, which is an improvement of Pang and Zalcman's theorem in some sense. Meanwhile, several examples are provided to show that our…

We show that the Eisenbud-Goto conjecture holds for (homogeneous) seminormal simplicial affine semigroup rings. Moreover, we prove an upper bound for the Castelnuovo-Mumford regularity in terms of the dimension, which is similar as in the…