Ideals of Lattice Ordered Monoid
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Date
2017-08
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Addis Ababa University
Abstract
In this project the notion of an ideal of a lattice ordered monoid A is introduced.
The notion of congruence relations on a lattice ordered monoid (l-monoid) A is also
introduced and its relation with ideals of A is investigated. In addition, we will
introduce the notion of normal ideals of lattice ordered monoid and dually
residuated lattice ordered monoid (DRl-monoid) in order to study their connection
with congruence relations. The ideal induced by congruence relations on an lmonoid
need not be normal. By imposing additional conditions on the congruence
relations on a DRl-monoid, we will prove that the induced ideal will be normal.
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Ideals of Lattice Ordered Monoid