If R is a ring and S is a subring of R, then S is  an R-module (module over R).

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.1: Definition Of A Ring
Problem 17E: If R1 and R2 are subrings of the ring R, prove that R1R2 is a subring of R.
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If R is a ring and S is a subring of R, then S is  an R-module (module over R).

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