Abstract
In this paper, the ordinal sum of quantales is provided. Based on this, the ordinal sums of many familiar ordered algebraic structures can be obtained, such as complete residuated lattice, spatial quantale, etc. Then we investigate the relationship between the quantale completion of partially ordered semigroups and the ordinal sum, and prove that for any family of two-side posemigroups, the ordinal sum of their quantale completions coincides with the quantale completion of their ordinal sum.
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