MATHEMATICA BOHEMICA, Vol. 132, No. 4, pp. 369-387 (2007)

On ideals of lattice ordered monoids

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

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