Browsing by Author "Baye, Alemu"
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Item Ideals of Lattice Ordered Monoid(Addis Ababa University, 2017-08) Baye, Alemu; Bekele, Berhanu (PhD)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.