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Ideals of noncommutative \(DR\ell\)-monoids. (English) Zbl 1081.06017
Summary: In this paper, we introduce the concept of an ideal of a noncommutative dually residuated lattice-ordered monoid, and we show that congruence relations and certain ideals are in a one-to-one correspondence.

MSC:
06F05 Ordered semigroups and monoids
06D35 MV-algebras
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References:
[1] A. Di Nola, G. Georgescu and A. Iorgulescu: Pseudo BL-algebras: Part I. Mult. Val. Logic 8 (2002), 673-714. · Zbl 1028.06007
[2] A. Dvure?enskij: On pseudo MV-algebras. Soft Comp. 5 (2001), 347-354. · Zbl 0998.06010 · doi:10.1007/s005000100136
[3] A. Dvure?enskij: Pseudo MV-algebras are intervals in ?-groups. J. Austral. Math. Soc. 72 (2002), 427-445. · Zbl 1027.06014 · doi:10.1017/S1446788700036806
[4] G. Georgescu and A. Iorgulescu: Pseudo MV-algebras. Mult. Val. Logic 6 (2001), 95-135. · Zbl 1014.06008
[5] G. Gr?tzer: General Lattice Theory. Birkh?user-Verlag, Basel-Boston-Berlin, 1998.
[6] I. Chajda: Congruence kernels in weakly regular varieties. Southeast Asian Bull. Math. 24 (2000), 15-18. · Zbl 0988.08002 · doi:10.1007/s10012-000-0015-8
[7] I. Chajda, R. Hala? and J. Rach?nek: Ideals and congruences in generalized MV-algebras. Demonstratio Math. 33 (2000), 213-222.
[8] T. Kov??: A general theory of dually residuated lattice ordered monoids. PhD. Thesis. Palack? Univ. Olomouc, 1996.
[9] J. Rach?nek: Prime ideals in autometrized algebras. Czechoslovak Math. J. 112 (1987), 65-69. · Zbl 0692.06007
[10] J. Rach?nek: A non-commutative generalization of MV-algebras. Czechoslovak Math. J. 52 (2002), 255-273. · Zbl 1012.06012 · doi:10.1023/A:1021766309509
[11] K. L. N. Swamy: Dually residuated lattice ordered semigroups I. Math. Ann. 159 (1965), 105-114. · Zbl 0135.04203 · doi:10.1007/BF01360284
[12] K. L. N. Swamy: Dually residuated lattice ordered semigroups III. Math. Ann. 167 (1966), 71-74. · Zbl 0158.02601 · doi:10.1007/BF01361218
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