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A First Course in Topology

"Let K be a field, and R = K[x_1, ..., x_n] a finitely generated K-algebra. Then R is a field implies R is algebraic over K."

"Let K be a field, and R = K[x_1, ..., x_n] a finitely generated K-algebra. Then R is a field implies R is algebraic over K."

Divisible Modules

"Let M be an R-module where R is a PID. We say that M is divisible if for each nonzero a in R, aM = M."