• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.1-11
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• 2009

The notion of a BCK-algebra with supremum (briefly, sBCK-algebra) is introduced, and several examples are given. Related properties are investigated. We show that every sBCK-algebra with an additional condition has the condition (S). The notion of a dry ideal of an sBCK-algebra is introduced. Conditions for an sBCK-algerba to be an spBCK-algebra are provided. We show that every sBCK-algebra satisfying additional condition is a semi-Brouwerian algebra.