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  • Thesis

  • Authors: Alahmadi, Adel Naif M. (2006)

  • Almost self-injective, continuous, quasi-continuous (also known as 7r-injective), and CS modules are generalizations of injective modules. The main aim of this dissertation is to study almost self-injective, continuous, quasi-continuous, and CS group rings. CS group algebras were initiated by Jain et. al [24]. They showed that K[D1] is a CS group algebra if and only if char(K) =6 2. Behn extended this result and showed that if K[G] is a prime group algebra with G polycyclic-by-finite, then K[G] is a CS-ring if and only if G is torsion-free or G '= D1 and char(K) =6 2 [5]. As a consequence, such a group algebra K[G] is hereditary excepting possibly when K[G] is a domain. We show that if K[G] is a semiprime group algebra of polycyclic¬by-finite group G and if K[G] has no direct summan...