Geodesic
On ideals of lattice ordered monoids
Mathematica Bohemica, Tome 132 (2007) no. 4, pp. 369-387

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In the paper the notion of an ideal of a lattice ordered monoid $A$ is introduced and relations between ideals of $A$ and congruence relations on $A$ are investigated. Further, it is shown that the set of all ideals of a soft lattice ordered monoid or a negatively ordered monoid partially ordered by inclusion is an algebraic Brouwerian lattice.
In the paper the notion of an ideal of a lattice ordered monoid $A$ is introduced and relations between ideals of $A$ and congruence relations on $A$ are investigated. Further, it is shown that the set of all ideals of a soft lattice ordered monoid or a negatively ordered monoid partially ordered by inclusion is an algebraic Brouwerian lattice.
DOI : 10.21136/MB.2007.133965
Classification : 06F05
Keywords: lattice ordered monoid; ideal; normal ideal; congruence relation; dually residuated lattice ordered monoid 
Jasem, Milan. On ideals of lattice ordered monoids. Mathematica Bohemica, Tome 132 (2007) no. 4, pp. 369-387. doi: 10.21136/MB.2007.133965
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[1] G. Birkhoff: Lattice Theory. Third edition, Amer. Math. Soc., Providence, 1967. | MR | Zbl

[2] A. Dvurečenskij: Pseudo MV-algebras are intervals in l-groups. J. Austral. Math. Soc. 72 (2002), 427–445. | DOI | MR

[3] G. Georgescu, A. Iorgulescu: Pseudo MV-algebras. Mult.-Valued Log. 6 (2001), 95–135. | MR

[4] G. Grätzer: General Lattice Theory. Akademie-Verlag, Berlin, 1978. | MR

[5] M. Hansen: Minimal prime ideals in autometrized algebras. Czech. Math. J. 44 (1994), 81–90. | MR | Zbl

[6] M. Jasem: On lattice-ordered monoids. Discuss. Math. Gen. Algebra Appl. 23 (2003), 101–114. | DOI | MR | Zbl

[7] M. Jasem: On polars and direct decompositions of lattice ordered monoids. Contributions to General Algebra 16, Verlag Johannes Heyn, Klagenfurt, 2005, pp. 115–131. | MR | Zbl

[8] T. Kovář: A General Theory of Dually Residuated Lattice Ordered Monoids. Doctoral Thesis, Palacký Univ., Olomouc, 1996.

[9] J. Kühr: Dually Residuated Lattice Ordered Monoids. Doctoral Thesis, Palacký Univ., Olomouc, 2003. | MR | Zbl

[10] J. Kühr: Ideals of non-commutative DRl-monoids. Czech. Math. J. 55 (2005), 97–111. | DOI | MR

[11] J. Kühr: Prime ideals and polars in DRl-monoids and pseudo BL-algebras. Math. Slovaca 53 (2003), 233–246. | MR

[12] J. Rachůnek: Prime ideals in autometrized algebras. Czech. Math. J. 37 (1987), 65–69.

[13] K. L. M. Swamy: Dually residuated lattice ordered semigroups. Math. Ann. 159 (1965), 105–114. | DOI | MR | Zbl

[14] D. Šalounová: Lex-ideals of DRl-monoids and GMV-algebras. Math. Slovaca 53 (2003), 321–330. | MR

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