Ring coproducts embedded in power-series rings
Ring coproducts embedded in power-series rings
Let $R$ be a ring (associative, with 1), and let $R<< a,b>>$ denote the power-series $R$-ring in two non-commuting, $R$-centralizing variables, $a$ and $b$. Let $A$ be an $R$-subring of $R<< a>>$ and $B$ be an $R$-subring of $R<< b>>$, and let $\alpha$ denote the natural map $A \amalg_R B …