Affine semiprime algebras of GK dimension one are (still) pi

Hopfian and Bassian algebras

A ring $A$ is called Hopfian if $A$ cannot be isomorphic to a proper homomorphic image $A/J$. $A$ is called Bassian if there cannot be an injection of $A$ into a proper homomorphic image $A/J$. We consider classes of Hopfian and Bassian rings, and tie representability of algebras and chain conditions on ideals to these properties. In particular, any semiprime algebra satisfying the ACC on semiprime ideals is Hopfian, and any semiprime affine PI-algebra over a field is Bassian.

量子线性空间的素与半素 smash 积

Prime and semiprime quantum linear space smash products

本文研究量子线性空间玻色子化与结合代数的 smash 积，给出其为（半）素的条件，并应用于量子仿射空间，推广了 Bergen 的结果。

Prime affine algebras of GK dimension two which are almost PI algebras

An almost PI algebra is a generalisation of a just infinite algebra which does not satisfy a polynomial identity. An almost PI algebra has some nice properties: It is prime, has a countable cofinal subset of ideals and when satisfying ACC(semiprimes), it has only countably many height 1 primes. Consider an affine prime Goldie non-simple non-PI $k$-algebra $R$ of GK dimension $<3$, where $k$ is an uncountable field. $R$ is an almost PI algebra. We give some possible additional conditions which make such an algebra primitive. This gives a partial answer to Small's question: Let $R$ be an affine …

仿射空间上的Lie括号与Nijenhuis括号

Lie and Nijenhuis brackets on affine spaces

本文通过堆运算将Lie代数推广至仿射空间，定义不依赖零元的Lie仿射代数，并证明Nijenhuis括号在其上满足相容性条件。

关于有限 Mal'cev 代数的多项式完备性

On polynomial completeness properties of finite Mal'cev algebras

本文研究有限 Mal'cev 代数的多项式完备性，将 E. Aichinger 和 P. Idziak 对严格 1-仿射完备扩张群的刻画推广至有限同余正则 Mal'cev 代数。

实现仿射基准的扩张：低维上同调

Extension realizing affine datum: low-dimensional cohomology

该研究针对泛代数簇构建低维上同调理论，刻画实现仿射基准的扩张，证明带弱差项簇中此类扩张等价于带阿贝尔核的扩张，引入作用概念并刻画中心扩张，还在子类中重现相关扩张表示特例。