Iranian Mathematical Society Journal of the Iranian Mathematical Society 2717-1612 5 1 2024 01 01 On Infinite direct products of Rings modulo their direct sums 21 31 180878 10.30504/jims.2023.409975.1138 EN E. Momtahan Department of Mathematics‎, ‎Yasouj University, Yaouj‎, ‎Iran. Journal Article 2023 08 03 In this article, inspiring with a result due to O.A.S. Karamzadeh, we examine the $\prod_{i\in I} R_i/\oplus_{i\in I} R_i$, where $\{R_i\}_{i\in I}$ is an infinite family of rings. We observe that they are not self-injective on either side. In some important cases they are however $\aleph_0$-self-injective. Along this line, we study the interconnection between regularity(in the sense of von Neumann), injectivity and $\aleph_0$-injectivity. https://jims.ims.ir/article_180878_4fb6455e0132c79627e7ef6606d20016.pdf