ON STRONGLY AND SEPARABLY ?1-p?+n-PROJECTIVE ABELIAN p-GROUPS

Let n>= 0 be an arbitrary integer. We prove some results for stronglyn-simply presented abelian p-groups with C-decomposable property, extending classical achievements due to Keef in Commun. Algebra (1990).As applications we define the classes of strongly ?1-p?+n-projective andseparably ?1-p?+n-projective abelian p-groups which are also properlycontained in all ?1-p?+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.

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