Abstract
In this paper, we consider the cancellation problem for direct products in the category of quantales. It is easy to see that quantales are not always cancelable. We show that indecomposable quantales, simple quantales, quantales without zero-divisors and quantales without nontrivial idempotent elements except the top element are cancelable. We also prove that each quantale can be embedded into a (unital) cancelable quantale.
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