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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

Consider the sequence in $ \Bbb N\times\Bbb N$ : $ (0,0),(0,1),(1,0),(0,2),(1,1),(2,0),(0,3),(1,2),(2,1),(3,0),(0,4),(1,3),(2,2),(3,1),(4,0),(0,5),(1,4),(2,3),(3,2),(4,1),(5,0),…,(0,2k-1),(1,2k-2),(2,2k-3),…,(k-1,k),(k,k-1),…,(2k-3,2),(2k-2,1),(2k-1,0),(0,2k),(1,2k-1),(2,2k-2),…,(k,k),…(2k-2,2),(2k-1,1),(2k,0),…$ Question: To define an Abelian group structure on $ \Bbb N$ that is not a finitely generated Abelian group, I need to know: what is rule of this sequence?Read more