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Radicals in non-commutative generalizations of MV-algebras
Mathematica slovaca, Tome 52 (2002) no. 2, pp. 135-144
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Rachůnek, Jiří. Radicals in non-commutative generalizations of MV-algebras. Mathematica slovaca, Tome 52 (2002) no. 2, pp. 135-144. http://geodesic.mathdoc.fr/item/MASLO_2002_52_2_a1/

[1] ABRUSCI V. M., RUET P.: Non-commutative logic I: the multiplicative fragment. Ann. Pure Appl. Logic 101 (2000), 29-64. | MR | Zbl

[2] ANDERSON M., FEIL T.: Lattice-Ordered Groups. D. Reidel Publ., Dordrecht, 1988. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[6] CETERCHI R.: Pseudo-Wajsberg algebras. Multiple-Valued Logic 6 (2001), 67-88. | MR | Zbl

[7] CETERCHI R.: The lattice structure of pseudo-Wajsberg algebras. J. UCS 6 (2000), 22-38. | MR | Zbl

[8] CHANG C. C.: Algebraic analysis of many valued logic. Trans. Amer. Math. Soc. 88 (1958), 467-490. | MR

[9] CHANG C. C.: A new proof of the completeness of the Lukasiewicz axioms. Trans. Amer. Math. Soc. 93 (1959), 74-80. | MR | Zbl

[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. | MR | Zbl

[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. | MR

[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. | MR | Zbl

[13] DVUREČENSKIJ A.: Pseudo $MV$-algebras are intervals in $\ell$-groups. J. Austral. Math. Soc 72 (2002) (To appеar). | Zbl

[14] DVUREČENSKIJ A.: States on pseudo MV-algebras. Studia Logica 68 (2001), 301-327. | MR | Zbl

[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.

[17] GEORGESCU G., IORGULESCU A.: Pseudo-MV algebras. Multiplе-Valued Logic 6 (2001), 95-135. | MR | Zbl

[18] GLASS A. M. W.: Partially Ordered Groups. World Sciеntific, Singaporе-New Jеrsey-London-Hong Kong, 1999. | MR | Zbl

[19] GOODEARL K. R.: Partially Ordered Abelian Groups with Interpolation. Math. Survеys Monographs 20, Amer. Math. Soc., Providеncе, RI, 1986. | MR | Zbl

[20] HÁJEK P.: Metamathematics of Fuzzy Logic. Kluwеr, Amstеrdam, 1998. | Zbl

[21] HORT D., RACHŮNEK J.: Lex ideals of generalized MV-algebras. In: Discrete Math. Theoret. Comput. Sci. (DTMCS01), Springer, London, 2001, pp. 125 -136. | MR | Zbl

[22] KOPYTOV V. M., MEDVEDEV N. YA.: The Theory of Lattice Ordered Groups. Kluwеr Acad. Publ., Dordrecht-Boston-London, 1994. | MR | Zbl

[23] LAMBEK J.: Some lattice models of bilinear logic. Algebra Universalis 34 (1995), 541-550. | MR | Zbl

[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. | MR | Zbl

[25] MAIELI R., RUET P.: Non-commutative logic III: focusing proofs. Prеprint. | Zbl

[26] MUNDICI D.: Interpretation of AF C* -algebras in Łukasiewicz sentential calculus. J. Funct. Anal. 65 (1986), 15-63. | MR

[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. | MR

[31] TURUNEN E.: Mathematics Behind Fuzzy Logic. Physica-Verlag, А Springеr-Vеrlag Comp., Hеidelbеrg-New York, 1999. | MR | Zbl

[32] YETTER D. N.: Quantales and (non-commutative) linear logic. J. Symbolic Logic 55 (1990), 41-64. | MR