Abstract: In this paper, we are interested in the following general question: Given a module M which has finite hollow dimension and which has a finite collection of submodules K_i (1≤i≤n) such that M=K₁+...+K_n, can we find an expression for the hollow dimension of M in terms of hollow dimensions of modules built up in some way from K₁,...,K_n We prove the following theorem: Let M be an amply supplemented module having finite hollow dimension and let K_i (1≤i≤n) be a finite collection of submodules of M such that M=K₁+...+K_n. Then the hollow dimension h(M) of M is the sum of the hollow dimensions of K_i (1≤i≤n) if and only if K_i is a supplement of K₁+...+K_i−1+K_i+1+...+K_n in M for each 1≤i≤n.

Key words: Hollow dimension, Supplement submodule

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