# ring theory – \$ R \$ – ideal algebra generated by a set

Leave $$R$$ be a unital ring, and $$S subset R$$. The two-sided ideal that I generated $$S$$ is the set of all form elements $$displaystyle sum_ {finite} a_is_ib_i$$ where $$a_i, b_i in R$$ Y $$s_i in S$$.

Leave $$R$$ be a commutative unital ring and $$A$$ be an algebra about $$R$$. Leave $$S subset A$$ Y $$I$$ be double $$R$$– ideal algebra generated by $$S$$. It is true that $$I$$ is the set of all form elements $$displaystyle sum_ {finite} r_ia_is_ib_i$$ where $$r_i in R$$, $$a_i, b_i in A$$ Y $$s_i in S$$?