AI 中文总结
本文解决了几乎严格纯Anderson t-模的同构问题，证明纯t-模经基变换后同构于几乎严格纯t-模，并给出其同构于严格纯t-模的充要条件。
AI 中文摘要
在Abelian Anderson t-模理论中，纯Anderson t-模具有重要作用。Namoijam和Papanikolas还引入了严格纯t-模和几乎严格纯t-模的概念，它们是纯t-模的特殊类。众所周知，并非所有纯t-模都同构于严格纯t-模（例如Carlitz模的张量幂），但几乎严格纯t-模的相同问题尚未得到解答。本文证明，在域K上定义的每个纯Anderson t-模，在基变换到K的合适有限代数扩张后，确实同构于几乎严格纯Anderson t-模；同时还给出了该模同构于严格纯Anderson t-模的充要条件。
英文摘要
In the theory of abelian Anderson $t$-modules, pure Anderson $t$-modules play an important role. Namoijam and Papanikolas also introduced the notions of strictly pure and almost strictly pure $t$-modules which are special classes of pure $t$-modules. Whereas it is well known that not all pure $t$-modules are isomorphic to strictly pure ones (e.g.~the tensor powers of the Carlitz module), the same question for almost strictly pure $t$-modules was not answered yet. In this article, we show that every pure Anderson $t$-module defined over a field $K$ is indeed isomorphic to an almost strictly pure Anderson $t$-module after base change to a suitable finite algebraic extension of $K$. We also give a necessary and sufficient criterion when such an isomorphism to a strictly pure Anderson $t$-module is possible.
Comments24 pages
