Kühr, Jan Remarks on ideals in lower-bounded dually residuated lattice-ordered monoids. (English) Zbl 1071.06007 Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 43, 105-112 (2004). Dually residuated lattice-ordered monoids (DR\(\ell \)-monoids, for short) form a wide class of algebras containing, e.g., the classes of lattice-ordered groups, Brouwerian algebras, BL- and pseudo BL-algebras, MV- and GMV-algebras. The author describes connections between ideals of lower-bounded DR\(\ell\)-monoids and ideals of their lattice reducts and studies the sets of idempotent and Boolean elements in those DR\(\ell \)-monoids. Reviewer: Jiří Rachůnek (Olomouc) Cited in 1 Document MSC: 06F05 Ordered semigroups and monoids Keywords:DR\(\ell \)-monoid; ideal; prime ideal PDF BibTeX XML Cite \textit{J. Kühr}, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 43, 105--112 (2004; Zbl 1071.06007) Full Text: EuDML References: [1] Cignoli R. L. O., Mundici D., D’Ottaviano I. M. L.: Algebraic Foundations of Many-valued Reasoning. : Kluwer Acad. Publ., Dordrecht-Boston-London. 2000. [2] Georgescu G., Iorgulescu A.: Pseudo \(MV\)-algebras. Mult. Valued Log. 6 (2001), 95-135. · Zbl 1014.06008 [3] Kovář T.: A General Theory of Dually Residuated Lattice Ordered Monoids. Ph.D. Thesis, Palacký University, Olomouc, 1996. [4] Kühr J.: Ideals of noncommutative \(DR\ell \)-monoids. Czech. Math. J. · Zbl 1081.06017 [5] Kühr J.: Prime ideals and polars in \(DR\ell \)-monoids and pseudo \(BL\)-algebras. Math. Slovaca 53 (2003), 233-246. · Zbl 1058.06017 [6] Kühr J.: A generalization of \(GMV\)-algebras. · Zbl 1150.06012 [7] Rachůnek J.: \(DR\ell \)-semigroups and \(MV\)-algebras. Czech. Math. J. 48 (1998), 365-372. · Zbl 0952.06014 · doi:10.1023/A:1022801907138 [8] Rachůnek J.: \(MV\)-algebras are categorically equivalent to a class of \(DR\ell _{1(i)}\)-semigroups. Math. Bohem. 123 (1998), 437-441. · Zbl 0934.06014 [9] Rachůnek J.: Connections between ideals of non-commutative generalizations of \(MV\)-algebras and ideals of their underlying lattices. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 40 (2001), 195-200. · Zbl 1040.06005 [10] Rachůnek J.: A non-commutative generalization of \(MV\)-algebras. Czech. Math. J. 52 (2002), 255-273. · Zbl 1012.06012 · doi:10.1023/A:1021766309509 [11] Swamy K. L. N.: Dually residuated lattice ordered semigroups. Math. Ann. 159 (1965), 105-114. · Zbl 0138.02104 · doi:10.1007/BF01364335 · eudml:161279 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.