# Keyword: Dorroh extension

Description: Given a commutative ring $R$ and a (possibly nonunital) ring $S$ which is an $R$ module, the underlying set is $R\times S$. Addition: $(r,s)+(r',s')=(r+r', s+s')$. Multiplication: $(r,s)(r',s')=(rr', rs'+r's+ss')$