A non-commutative generalization of $MV$-algebras

 Access to full text

 Full (PDF)

1. Foundations of the Theory of Quasigroups and Loops, Nauka, Moscow, 1967. (Russian) (1967) MR0218483
2. Groupes et Anneaux Réticulés, SpringerVerlag, Berlin-Heidelberg-New York, 1977. (1977) MR0552653
3. A Course in Universal Algebra, Springer-Verlag, Berlin-Heidelberg-New York, 1981. (1981) MR0648287
4. 10.1090/S0002-9947-1958-0094302-9, Trans. Amer. Math. Soc. 88 (1958), 467–490. (1958) Zbl0084.00704MR0094302DOI10.1090/S0002-9947-1958-0094302-9
5. A new proof of the completeness of the Lukasiewicz axioms, Trans. Amer. Math. Soc. 93 (1959), 74–80. (1959) Zbl0093.01104MR0122718
6. Free lattice-ordered abelian groups and varieties of $MV$-algebras, Proc. IX. Latin. Amer. Symp. Math. Log., Part 1, Not. Log. Mat. 38 (1993), 113–118. (1993) Zbl0827.06012MR1332526
7. Lattice-Ordered Groups (Advances and Techniques), A. M. W. Glass and W. Charles Holland (eds.), Kluwer Acad. Publ., Dordrecht-Boston-London, 1989. (1989) Zbl0705.06001MR1036072
8. $MV$-algebras, ideals and semisimplicity, Math. Japon. 34 (1989), 563–583. (1989) Zbl0677.03041MR1005257
9. The Theory of Lattice Ordered Groups, Kluwer Acad. Publ., Dordrecht-Boston-London, 1994. (1994) MR1369091
10. A general theory of dually residuated lattice ordered monoids, Thesis, Palacký University Olomouc, 1996. (1996) 
11. Interpretation of $AF{C}^{*}$-algebras in Łukasiewicz sentential calculus, J. Funct. Anal. 65 (1986), 15–63. (1986) Zbl0597.46059MR0819173
12. $MV$-algebras are categorically equivalent to bounded commutative $BCK$-algebras, Math. Japon. 31 (1986), 889–894. (1986) Zbl0633.03066MR0870978
13. 10.1023/A:1022801907138, Czechoslovak Math. J. 48(123) (1998), 365–372. (1998) MR1624268DOI10.1023/A:1022801907138
14. $MV$-algebras are categorically equivalent to a class of $DR{l}_{1\left(i\right)}$-semigroups, Math. Bohem. 123 (1998), 437–441. (1998) MR1667115
15. Dually residuated lattice ordered semigroups, Math. Ann. 159 (1965), 105–114. (1965) Zbl0138.02104MR0183797
16. 10.1007/BF01364335, Math. Ann. 160 (1965), 64–71. (1965) MR0191851DOI10.1007/BF01364335
17. 10.1007/BF01361218, Math. Ann. 167 (1966), 71–74. (1966) Zbl0158.02601MR0200364DOI10.1007/BF01361218

1. Magdalena Wojciechowska-Rysiawa, IF-filters of pseudo-BL-algebras
2. Grzegorz Dymek, On fuzzy ideals of pseudo MV-algebras
3. Andrzej Walendziak, On maximal ideals of pseudo-BCK-algebras
4. Jiří Rachůnek, Connections between ideals of non-commutative generalizations of $MV$-algebras and ideals of their underlying lattices
5. Jiří Rachůnek, Radicals in non-commutative generalizations of MV-algebras
6. Anatolij Dvurečenskij, States on unital partially-ordered groups
7. P. Emanovský, Jiří Rachůnek, A non commutative generalization of $☆$-autonomous lattices
8. Jiří RACHŮNEK, Dana ŠALOUNOVÁ, Approximation Spacesin Non-commutative Generalizations of $MV$-algebras
9. Grzegorz Dymek, Noetherian and Artinian pseudo MV-algebras
10. Ivan Chajda, Miroslav Kolařík, Remarks on pseudo MV-algebras