ON STRONGLY AND SEPARABLY ω1-p^(ω+n) -PROJECTIVE ABELIAN p-GROUPS

Let n ≥ 0 be an arbitrary integer. We prove some results for strongly n-simply presented abelian p-groups with C-decomposable property, extending classical achievements due to Keef in Commun. Algebra (1990). As applications we dene the classes of strongly p^(ω+n) -projective and separably p^(ω+n) -projective abelian p-groups which are also properly contained in all p^(ω+n) -projectives, recently defined by Keef in J. Alg. Numb. Th. Acad. (2010). Moreover, some principal descriptions concerning these new objects are obtained as well.