Abstract Algebra: Theory and Applications · Problem 24

Polynomials — Thomas Judson

Mathematics — Abstract Algebra · subrings

Problem

Let

R

be a ring with a collection of subrings

\{R_\alpha\}

. Prove that

\cap R_\alpha

is a subring of

R

. Give an example to show that the union of two subrings is not necessarily a subring.