Alahmadi, A. N.; Jain, S. K.; Kanwar, P.; Srivastava, J. B. Group algebras in which complements are summands. (Russian, English) Zbl 1110.16024 Fundam. Prikl. Mat. 11, No. 3, 3-11 (2005); translation in J. Math. Sci., New York 144, No. 2, 3875-3880 (2007). Let \(G\) be a group, and let \(KG\) be its group algebra over some field \(K\). A ring \(R\) is said to be almost self-injective if for any right ideal \(H\) of \(R\) and every \(R\)-homomorphism \(f\colon H\to R\), there exists an \(R\)-homomorphism \(g\colon R\to R\) such that \(g\circ f=\text{id}_H\). The paper studies the following problems: (1) When is \(KG\) almost self-injective? (2) When is \(KG\) continuous? The authors show that every almost self-injective algebra is self-injective, and if \(KG\) is continuous, then \(G\) is locally finite. Reviewer: S. A. Vakhrameev (Moskva) Cited in 1 Document MSC: 16S34 Group rings 16D50 Injective modules, self-injective associative rings 20C07 Group rings of infinite groups and their modules (group-theoretic aspects) Keywords:group algebras; almost self-injectivity; local finiteness; CS-rings; almost selfinjective rings; continuous rings PDFBibTeX XMLCite \textit{A. N. Alahmadi} et al., Fundam. Prikl. Mat. 11, No. 3, 3--11 (2005; Zbl 1110.16024); translation in J. Math. Sci., New York 144, No. 2, 3875--3880 (2007) Full Text: EMIS