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In this paper, the notions of regular, completely regular, compact additive generalized algebraic lattices () are introduced, and Stone compactification is constructed. The following theorem is also obtained. Theorem: An additive generalized algebraic lattice has a Stone compactification if and only if it is regular and completely regular. 2000 AMS Classification: 06B30, 06B35, 54D35, 54H10doi:10.4995/agt.2007.1901 fatcat:kwn4vqhahzbmlbhmyy3oyzw634