相关论文: Additivity of Jordan Elementary Maps on Rings

A ring is *unit-additive* if a sum of units is always either a unit or nilpotent. For example, $k[X]$ and $k[X]/(X^2)$ are unit-additive, but $\mathbb Z$ is not. We prove a wide-ranging theorem about unit-additivity in semigroup rings,…

Let $R$ be an affine domain of characteristic zero with finite quotients. We prove that a polynomial map over $R$ is surjective if and only if it is surjective over $\hat{R_{\mathfrak{m}}}$, the completion of $R$ with respect to…

Any Jordan curve in the complex plane can be approximated arbitrarily well in the Hausdorff topology by Julia sets of polynomials. Finite collections of disjoint Jordan domains can be approximated by the basins of attraction of rational…

An additive action on an algebraic variety is an effective action of the vector group with an open orbit. We describe projective surfaces with du Val singularities that admit an additive action with a finite number of orbits. In particular,…

We show that the map $\pi_\ast \mathrm{MString}\to \pi_\ast \mathrm{tmf}$ induced by the Ando-Hopkins-Rezk orientation is surjective. This proves an unpublished claim of Hopkins and Mahowald. We do so by constructing an $\mathbf{E}_1$-ring…

We investigate flat maps where the source or target is a Noetherian ring, giving necessary and/or sufficient conditions on a ring for such maps to exist. Along the way, we develop some general facts about flat ring maps, and exhibit many…

In this article, we develop the Yoccoz puzzle technique to study a family of rational maps termed McMullen maps. We show that the boundary of the immediate basin of infinity is always a Jordan curve if it is connected. This gives a positive…

In this paper, we extend the theory of special local Moufang sets. We construct a local Moufang set from every local Jordan pair, and we show that every local Moufang set satisfying certain (natural) conditions gives rise to a local Jordan…

The notion of derivation with invertible values as a derivation of ring with unity that only takes multiplicatively invertible or zero values appeared in a paper of Bergen, Herstein and Lanski, in which they determined the structure of…

Let $W$ be a quasiprojective variety over an algebraically closed field of characteristic zero. Assume that $W$ is birational to a product of a smooth projective variety $A$ and the projective line. We prove that if $A$ contains no rational…

In this paper we prove an asymptotically sharp Bernstein-type inequality for polynomials on analytic Jordan arcs. Also a general statement on mapping of a domain bounded by finitely many Jordan curves onto a complement to a system of the…

We elucidate the geometry of matrix models based on simple formally real Jordan algebras. Such Jordan algebras give rise to a nonassociative geometry that is a generalization of Lorentzian geometry. We emphasize constructions for the…

Since for the classification of finite (congruence-)simple semirings it remains to classify the additively idempotent semirings, we progress on the characterization of finite simple additively idempotent semirings as semirings of…

In this paper we are concerned with the finiteness property of Ext-indices of several ring extensions. In this direction, we introduce some conjectures and discuss the relationship of them. Also we give affirmative answers to these…

In this paper, we establish two results concerning algebraic $(\mathbb{C},+)$-actions on $\mathbb{C}^n$. First let $\phi$ be an algebraic $(\mathbb{C},+)$-action on $\mathbb{C}^3$. By a result of Miyanishi, its ring of invariants is…

We prove results on fibers of polynomial mappings Rn ! Rn and deduce when such mappings are surjective under certain conditions.

We obtain general upper bounds of the sizes and the numbers of Jordan blocks for the eigenvalues $\lambda \not= 1$ in the monodromies at infinity of polynomial maps.

This paper proves finite generation of the log canonical ring without Mori theory.

We talk about the image of the Hilbert map. We show the necessary and sufficient condition that the Hilbert map is surjective.

We prove the existence of rational maps having smooth degenerate Herman rings. This answers a question of Eremenko affirmatively. The proof is based on the construction of smooth Siegel disks by Avila, Buff and Ch\'{e}ritat as well as the…