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directoid; relatively pseudocomplemented directoid; congruence distributivity; $3$-permutability; residuated structure; adjointness property; variety

References:

[1] Chajda, I.: **An extension of relative pseudocomplementation to non-distributive lattices**. Acta Sci. Math. (Szeged) 69 (2003), 491-496. MR 2034188 | Zbl 1048.06005

[2] Chajda, I.: **Pseudocomplemented directoids**. Comment. Math. Univ. Carol. 49 (2008), 533-539. MR 2493936 | Zbl 1212.06005

[3] Chajda, I.: **Relatively pseudocomplemented directoids**. Comment. Math. Univ. Carol. 50 (2009), 349-357. MR 2573409 | Zbl 1212.06004

[4] Chajda, I., Eigenthaler, G., Länger, H.: **Congruence Classes in Universal Algebra**. Heldermann Lemgo (2003), 217. MR 1985832 | Zbl 1014.08001

[5] Chajda, I., Halaš, R., Kühr, J.: **Semilattice Structures**. Heldermann Lemgo (2007), 228. MR 2326262 | Zbl 1117.06001

[6] Hagemann, J., Mitschke, A.: **On $n$-permutable congruences**. Algebra Universalis 3 (1973), 8-12. DOI 10.1007/BF02945100 | MR 0330010 | Zbl 0273.08001

[7] Ježek, J., Quackenbush, R.: **Directoids: Algebraic models of up-directed sets**. Algebra Universalis 27 (1990), 49-69. DOI 10.1007/BF01190253 | MR 1025835

[8] Jones, G. T.: **Pseudo-complemented Semi-lattices**. Ph.D. Thesis Univ. of California, Los Angeles (1972). MR 2622711