Continuous solutions to algebraic forcing equations

Normality and Related Properties of Forcing Algebras

We present a sufficient condition for irreducibility of forcing algebras and study the (non)-reducedness phenomenon. Furthermore, we prove a criterion for normality for forcing algebras over a polynomial base ring with coefficients in a perfect field. This gives a geometrical normality criterion for algebraic (forcing) varieties over algebraically closed fields. Besides, we examine in detail an specific (enlightening) example with several forcing equations. Finally, we compute explicitly the normalization of a particular forcing algebra by means of finding explicitly the generators of the idea…

Algebraic Characterization of Rings of Continuous p-adic Valued Functions

The aim of this paper is to give an algebraic characterization of the rings $C(X,\mathbb{Q}_p)$ of all continuous $\mathbb{Q}_p$-valued functions on a compact space $X$. The characterization is similar to that of M. Stone from 1940 for the case of $\mathbb{R}$-valued functions.

几何连续样条的代数框架

An algebraic framework for geometrically continuous splines

本文提出一个代数框架，通过链复形和同调工具分析几何连续$G^r$-样条空间，给出连续性判据、基构造算法和维数公式，推广了Billera-Schenck-Stillman复形。

关于哥德巴赫猜想的一些代数与几何推广

On some algebraic and geometric extensions of Goldbach's conjecture

本文研究域上仿射代数簇正则函数环的哥德巴赫猜想，定义牛顿多面体的哥德巴赫条件，构造性证明任意至少两个变量的多项式可表示为至多2r个绝对不可约多项式之和，并验证强迫代数及局部化等情形。