Kühr, Jan Ideals of noncommutative \(DR\ell\)-monoids. (English) Zbl 1081.06017 Czech. Math. J. 55, No. 1, 97-111 (2005). 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. Cited in 11 Documents MSC: 06F05 Ordered semigroups and monoids 06D35 MV-algebras Keywords:dually residuated lattice-ordered monoid; ideal; normal ideal PDF BibTeX XML Cite \textit{J. Kühr}, Czech. Math. J. 55, No. 1, 97--111 (2005; Zbl 1081.06017) Full Text: DOI EuDML 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.