Residual smallness in commutative algebra

In Oman and Salminen 19 Oman, G., Salminen, A. Residually small commutative rings. J. Commut. Algebra (17 pages as a preprint, to appear). Google Scholar]], the authors introduce and study residually small rings, defined as follows: an infinite commutative ring R with identity is residually smallif for every r∈R?{0}, there exists an ideal I_r of R such that r?I_r and |R∕I_r|<|R|. The purpose of this note is to extend our study. In particular, we continue our investigation of residually small rings and then generalize this notion to modules.