On Infinite direct products of Rings modulo their direct sums

Document Type : Dedicated to Prof. O. A. S. Karamzadeh


Department of Mathematics‎, ‎Yasouj University, Yaouj‎, ‎Iran.


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.


Main Subjects

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