Artin-Schelter正则代数是几何思想运用于非交换代数研究的重要实现，它的分类、构造和性质研究已成为非交换射影几何领域的重要课题。本项目主要从Artin-Schelter正则代数的构造和性质两方面展开，研究内容包括：1)代数smash积在Artin-Schelter正则代数构造上的运用，以实现一般高维Artin-Schelter正则代数的发现；2）研究适当的代数形变构造方法，在保持原有属性的前提下，从具有良好性质的Artin-Schelter正则代数类出发构造新Artin-Schelter正则代数；3）在前两者基础上，考察这些构造方法的环理论和同调性质，尤其是斜Calabi-Yau性质的讨论，并给出相应Nakayama自同构的刻画。对构造方法的研究，有助于更深入地理解Artin-Schelter正则代数，并丰富实例，驱动分类工作的进一步发展。

Artin-Schelter regular algebras are the important realization of the ideas which noncommutative algebraic geomerty furnishes for the study of noncommutative algebras. The classification, construction and properties of Artin-Schelter regular algebras are the valuable projects in noncommutative projective geometry. The proposal concerns mainly the construction and related properties of Artin-Schelter regular algebras. We study the following three topics: 1) Study Artin-Schelter regularity of the method called smash product of algebras. We expect this method to construct more general high dimensional Artin-Schelter regular algebras. 2) To gain new Artin-Schelter regular algebras with original properties by appropriate deformations of some certain classes of Artin-Schelter algebras with nice properties. 3) We discuss ring-theoretic and homological properties of such methods, especially the skew Calabi-Yau property and description of Nakayama automorphisms. The study of construction will benefit to the understanding of Artin-Schelter regular algebras, provide ample examples and develop the work of classification.