Let $B = \{ \{a + b f_i(n) : n\in \Bbb{Z}\} : a,(b\neq 0) \in \Bbb{Z}, f_i \in F \}$. Then what are necessary and sufficient conditions on the set of integer functions $F$ such that $B$ is a basis for a topological ring on $\Bbb{Z}$? Let me know also if there's a better way of setting all this up. Thanks.
2026-03-25 06:12:13.1774419133
Neccessary and sufficient conditions to form a topological ring on $\Bbb{Z}$?
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