Abstract
We identify the $${{}^\star}$$?-ideals of a distributive demi-pseudocomplemented algebra L as the kernels of the boolean congruences on L, and show that they form a complete Heyting algebra which is isomorphic to the interval $${[G,\iota]}$$[G,?] of the congruence lattice of L where G is the Glivenko congruence. We also show that the notions of maximal $${{}^\star}$$?-ideal, prime $${{}^\star}$$?-ideal, and falsity ideal coincide.
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