Radicals in non-commutative generalizations of MV-algebras

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1. ABRUSCI V. M., RUET P., Non-commutative logic I: the multiplicative fragment, Ann. Pure Appl. Logic 101 (2000), 29-64. Zbl0962.03054MR1729743
2. ANDERSON M., FEIL T., Lattice-Ordered Groups, D. Reidel Publ., Dordrecht, 1988. (1988) Zbl0636.06008MR0937703
3. BAUDOT R., Non-commutative logic programming language NoCLog, In: Symposium LICS 2000 (Santa Barbara). Short Presentations. 
4. BIGARD A., KEIMEL K., WOLFENSTEIN S., Groupes et Anneaux Réticulés, Springer-Verlag, Berlin-Heidelberg-New York, 1977. (1977) Zbl0384.06022MR0552653
5. CETERCHI R., On algebras with implications, categorically equivalent to pseudo-MV algebras, In: Proc. Fourth Inter. Symp. Econ. Inform., May 6-9, 1999, INFOREC Printing House, Bucharest, 1999, pp. 912-917. (1999) Zbl0984.06008MR1730094
6. CETERCHI R., Pseudo-Wajsberg algebras, Multiple-Valued Logic 6 (2001), 67-88. Zbl1013.03074MR1817437
7. CETERCHI R., The lattice structure of pseudo-Wajsberg algebras, J. UCS 6 (2000), 22-38. Zbl0963.06012MR1817730
8. CHANG C. C., Algebraic analysis of many valued logic, Trans. Amer. Math. Soc. 88 (1958), 467-490. (1958) MR0094302
9. CHANG C. C., A new proof of the completeness of the Lukasiewicz axioms, Trans. Amer. Math. Soc. 93 (1959), 74-80. (1959) Zbl0093.01104MR0122718
10. CIGNOLI R. O. L., D'OTTAVIANO I. M. L., MUNDICI D., Algebraic Foundations of Many-Valued Reasoning, Kluwеr Acad. Publ., Dordrecht-Boston-London, 2000. Zbl0937.06009MR1786097
11. CIGNOLI R., TORRENS A., The poset of prime $\ell$-ideals of an abelian $\ell$-group with a strong unit, J. Algebra 184 (1996), 604-614. (1996) MR1409232
12. DI NOLA A., GEORGESCU G., SESSA S., Closed ideals of MV-algebras, In: Advances in Contemporary Logic and Computer Sciеncе. Contеmp. Math. 235, Amеr. Math. Soc, Providеncе, RI, 1999, pp. 99-112. (1999) Zbl0937.06010MR1721208
13. DVUREČENSKIJ A., Pseudo $MV$-algebras are intervals in $\ell$-groups, J. Austral. Math. Soc 72 (2002) (To appеar). Zbl1027.06014
14. DVUREČENSKIJ A., States on pseudo MV-algebras, Studia Logica 68 (2001), 301-327. Zbl1081.06010MR1865858
15. DVUREČENSKIJ A., PULMANNOVÁ S., Nеw Trends in Quantum Structures, Kluwеr Acad. Publ., Dordrеcht-Boston-London, 2000. 
16. GEORGESCU G., IORGULESCU A., Pseudo-MV algebras: A non-commutative extension of MV-algebras, In: Proc Fourth Intеr. Symp. Econ. Inform., May 6-9, 1999, INFOREC Printing House, Bucharеst, 1999, pp. 961-968. (1999) 
17. GEORGESCU G., IORGULESCU A., Pseudo-MV algebras, Multiplе-Valued Logic 6 (2001), 95-135. Zbl1014.06008MR1817439
18. GLASS A. M. W., Partially Ordered Groups, World Sciеntific, Singaporе-New Jеrsey-London-Hong Kong, 1999. (1999) Zbl0933.06010MR1791008
19. GOODEARL K. R., Partially Ordered Abelian Groups with Interpolation, Math. Survеys Monographs 20, Amer. Math. Soc., Providеncе, RI, 1986. (1986) Zbl0589.06008MR0845783
20. HÁJEK P., Metamathematics of Fuzzy Logic, Kluwеr, Amstеrdam, 1998. (1998) Zbl0937.03030
21. HORT D., RACHŮNEK J., Lex ideals of generalized MV-algebras, In: Discrete Math. Theoret. Comput. Sci. (DTMCS01), Springer, London, 2001, pp. 125 -136. Zbl0983.06015MR1934826
22. KOPYTOV V. M., MEDVEDEV N. YA., The Theory of Lattice Ordered Groups, Kluwеr Acad. Publ., Dordrecht-Boston-London, 1994. (1994) Zbl0834.06015MR1369091
23. LAMBEK J., Some lattice models of bilinear logic, Algebra Universalis 34 (1995), 541-550. (1995) Zbl0840.03044MR1357483
24. LAMBEK J., Bilinear logic and Grishin algebras, In: Logic at Wгork. Essays Dedicated to the Memory of Helena Rasiowa (E. Orlowska, ed.), Physica-Verlag Comp., Heidelberg, 1999, pp. 604-612. (1999) Zbl0957.03063MR1720819
25. MAIELI R., RUET P., Non-commutative logic III: focusing proofs, Prеprint. Zbl1072.03035
26. MUNDICI D., Interpretation of AF C* -algebras in Łukasiewicz sentential calculus, J. Funct. Anal. 65 (1986), 15-63. (1986) MR0819173
27. RACHŮNEK J., A non-commutative generalгzation of MV-algebras, Czechoslovak Math. J. (To appear). 
28. RАCHŮNEK J., Prime ideals and polars in generalized MV-algebras, Multiple-Valued Logic (To appear). 
29. RАCHŮNEK J., Prime spectra of non-commutative generalгzations of MV-algebras, (Submitted). 
30. RUET P., Non-commutative logic II: sequent calculus and phrase semantics, Math. Structures Comput. Sci. 10 (2000), 277-312. MR1770234
31. TURUNEN E., Mathematics Behind Fuzzy Logic, Physica-Verlag, А Springеr-Vеrlag Comp., Hеidelbеrg-New York, 1999. (1999) Zbl0940.03029MR1716958
32. YETTER D. N., Quantales and (non-commutative) linear logic, J. Symbolic Logic 55 (1990), 41-64. (1990) MR1043543

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