论文标题
Noetherian pi-algebras的能力
Representability of Noetherian PI-algebras
论文作者
论文摘要
本说明涉及Noetherian pi-Algebras的代表性仍然开放的问题。扩展了罗文（Rowen）和小（对伯格曼（Bergman）的观察）的结果，即包含一个字段的通勤戒指上的每个有限生成的模块是可以表示的，我们为noeethian pi-algebra $ r $包含一个字段的代表性机械提供了一种，其中包括$ r $ r $是有限的（作为一个模块）的$ subalge subalge subalge usom cubalgerbra usomorphbra usorphbra usorphbra to $ insomorphra usorphbra。我们构建了一个不可证明的pi algebras家族，证明了这些结果的清晰度，以及一些众所周知的先前可说明性结果。
This note concerns the still open question of representability of Noetherian PI-algebras. Extending a result of Rowen and Small (with an observation of Bergman) that every finitely generated module over a commutative Noetherian ring containing a field is representable, we provide a representability machinery for a Noetherian PI-algebra $R$ containing a field, which includes the case that $R$ is finite (as a module) over a commutative subalgebra isomorphic to $R/N$. We construct a family of non-representable PI-algebras demonstrating the sharpness of these results, as well as of some well known previous representability results.
