• Honam Mathematical Journal
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• v.32 no.1
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• pp.141-155
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• 2010

In this paper we prove that with some hypothesis the set of k-isomorphism classes of simple closed k-surfaces in ${\mathbf{Z}}^3$ forms a commutative monoid with an operation derived from a digital connected sum, k ${\in}$ {18,26}. Besides, with some hypothesis the set of k-homotopy equivalence classes of closed k-surfaces in ${\mathbf{Z}}^3$ is also proved to be a commutative monoid with the above operation, k ${\in}$ {18,26}.