We shall define the infinitely-many-variable formal power series ring $ A = {\Bbb F}_q[[X_1,\ldots,X_{\infty}]]$ over a finite field $ {\Bbb F}_q$ as the following$ \colon$ $ A \colon= \underset{n \geq 1}{\varprojlim}\, {\Bbb F}_q[[X_1,\ldots,X_n]]$ . For example, $ \Sigma_{n = 1}^{n = \infty} X_n = X_1 + X_2 + \ldots \in A$ . The ring $Read more