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In this paper we get some properties which are compatible with the outer tensor product of local interior G-algebras in Section 2, in Section 3 we generalize the results of Külshammer in [2] on some indecomposable modules by the tool of inner tensor product of local interior G-algebras, we also discussed the centralizer C(A) of A in A for an interior G-algebra A in Section 4, which makes sense for the extended definition in Section 1.
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