De Morgan algebras with double demi-pseudocomplementation

The variety ddpM of de Morgan algebras with double demi-pseudocomplementation consists of those algebras (L; ∧, ∨, ∘,*, +, 0,1) of type (2,2,1,1,1,0,0) where (L; ∧, ∨, ∘,*, +, 0,1) is a de Morgan algebra, (L; ∧, ∨, ∘,*, +, 0,1) is a double demi-p-lattice and the operations x ↦ x∘, x ↦ x* and x ↦ x+ are linked by the identities x*∘ = x*∘, x+∘ =x∘+ and x*+ = x+*. In this paper, we characterize congruences on a ddpM-algebra, and give a description of the subdirectly irreducible algebras.