Locally Nilpotent Derivations, A New Ring Invariant and Applications

MAKAR-LIMANOV，摘要9700894 本文的主要研究对象是各种代数上的局部幂零导子，一个新的不变量，以及它们在代数和几何问题中的可能应用。这项研究的动机是发展代数工具，使人们能够区分环（在交换和非交换设置）。不变量最初是为了区分具有四个生成元的多项式环的某些因子环而引入的，在描述某类曲面的自同构群和消除型问题中也是有用的。 环论和群论提供了一种通过研究某些性质（如对称性和反射）来描述几何对象的方法，以及这些“操作”如何使研究对象的某些几何特征“不变”。

MAKAR-LIMANOV, ABSTRACT 9700894 The main objects of the research in this proposal are locally nilpotent derivations on various algebra, a new invariant which was recently introduced by the principal investigator, and their possible applications to algebraic and geometric questions. The motivation of this research is the development of algebraic tools which allow one to distinguish rings (in commutative and non-commutative settings). The invariant which was originally introduced in order to distinguish some factor-rings of a polynomial ring with four generators also is useful in a description of groups of automorphisms of a certain class of surfaces and in cancellation type problems. Ring theory and group theory provide a means for describing geometric objects through the study of certain properties like symmetry and reflections and how these "operations" leave "invariant" certain geometric features of the objects of study.