On weak injectivity of direct sums of modules (Q1275907)

This paper studies the concept of weak injectivity in the category \(\sigma[M]\). The question of direct sums of weakly injective modules being weakly injective is revisited through their study of weak injectivity in \(\sigma[M]\). The paper contains several interesting results, like obtaining necessary and sufficient conditions for \(\Sigma\)-weak injectivity of the injective hull of a simple module. A survey of results on weak injectivity is contained in [\textit{S. K. Jain, S. R. López-Permouth}, Computational Algebra, Lect. Notes Pure Appl. Math. 151, 205-232 (1993; Zbl 0802.16005)].