Hoops and their implicational reducts (abstract)

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1. [1] G. Birkhoff, Lattice Theory, Amer. Math. Soc. Colloq. Publ. 25, 3rd ed., Amer. Math. Soc., Providence 1967. 
2. [2] W. J. Blok and D. Pigozzi, Algebraizable Logics, Mem. Amer. Math. Soc. 396 (1989). Zbl0664.03042
3. [3] W. J. Blok and D. Pigozzi, On the structure of varieties with equationally definable principal congruences III, Algebra Universalis, to appear. Zbl0817.08004
4. [4] B. Bosbach, Komplementäre Halbgruppen. Kongruenzen und Quotienten, Fund. Math. 64 (1970), 1-14. 
5. [5] J. R. Büchi and T. M. Owens, Complemented monoids and hoops, unpublished manuscript. 
6. [6] C. C. Chang, A new proof of the completeness of the Łukasiewicz axioms, Trans. Amer. Math. Soc. 93 (1959), 74-80. Zbl0093.01104
7. [7] W. H. Cornish, A large variety of BCK-algebras, Math. Japon. 26 (1981), 339-342. Zbl0463.03039
8. [8] I. M. A. Ferreirim, On varieties and quasivarieties of hoops and their reducts, thesis, Univ. of Illinois at Chicago, 1992. 
9. [9] I. Fleischer, Every BCK-algebra is a set of residuables in an integral pomonoid, J. Algebra 119 (1988), 360-365. Zbl0658.06012
10. [10] H. Gaitan, Quasivarieties of Wajsberg algebras, J. Non-Classical Logic 8 (1991), 79-101. Zbl0772.06011
11. [11] D. Higgs, Dually residuated commutative monoids with identity element do not form an equational class, Math. Japon. 29 (1984), 69-75. Zbl0549.06009
12. [12] W. C. Holland, A. H. Mekler, and N. R. Reilly, Varieties of lattice-ordered groups in which prime powers commute, Algebra Universalis 23 (1986), 196-214. Zbl0598.06008
13. [13] Y. Komori, Super-Łukasiewicz implicational logics, Nagoya Math. J. 72 (1978), 127-133. Zbl0363.02015
14. [14] H. Ono and Y. Komori, Logics without the contraction rule, J. Symbolic Logic 50 (1985), 169-201. Zbl0583.03018
15. [15] M. Pałasiński, An embedding theorem for BCK-algebras, Math. Seminar Notes Kobe Univ. 10 (1982), 749-751. 
16. [16] R. Wójcicki, On matrix representations of consequence operations of Łukasiewicz's sentential calculi, Z. Math. Logik Grundlag. Math. 19 (1973), 239-247. Zbl0313.02008
17. [17] A. Wroński, An algebraic motivation for BCK-algebras, Math. Japon. 30 (1983), 187-193. Zbl0569.03029
18. [18] A. Wroński, BCK-algebras do not form a variety, ibid. 28 (1983), 211-213., Zbl0518.06014

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