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MATHEMATICA BOHEMICA, Vol. 132, No. 4, pp. 369-387 (2007)
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On ideals of lattice ordered monoids

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Milan Jasem

* Milan Jasem*, Institute of Information Engineering, Automation and Mathematics, Faculty of Chemical and Food Technology, Slovak Technical University, Radlinskeho 9, 812 37 Bratislava, Slovak Republic, e-mail: ` milan.jasem@stuba.sk`

**Abstract:** 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.

**Keywords:** lattice ordered monoid, ideal, normal ideal, congruence relation, dually residuated lattice ordered monoid

**Classification (MSC2000):** 06F05

**Full text of the article:**

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