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Ideals In Almost Distributive Lattice

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dc.contributor.author Abu-Ghalioon, Alaa
dc.date.accessioned 2022-05-24T06:58:49Z
dc.date.available 2022-05-24T06:58:49Z
dc.date.issued 2017-01-01
dc.identifier.uri http://localhost:8080/xmlui/handle/123456789/8497
dc.description no of pages 84, 30117, ماجستير رياضيات 1/2017
dc.description.abstract This thesis aims to develop a better understanding of Almost distributive lattice and its ideals. We present the definition of Almost distributive lattice, ideals and filters. Also we study some basic properties of Almost distributive lattice and give some examples on this class which includes almost all the existing ring theoretic generalisations of a Boolean ring like regular rings. The concepts of a-ideals, annihilator ideals, O-ideals and minimal prime ideals are defined, and we furnish the relation between these concepts. In addition It is proved that the set of all annihilator ideals of an Almost distributive lattice forms a complete Boolean algebra and the set of all a-ideals forms a complete distributive lattice. Also characterization theorems for each of these concepts are proved. Furthermore we present the definition of regular and 1r-regular ring, which are type of rings included by ADLs, The properties and characterizations theorems connecting between these concepts are studied, and several examples are given en_US
dc.language.iso en en_US
dc.publisher جامعة بوليتكنك فلسطين - ماجستير رياضيات en_US
dc.subject Distributive Lattice en_US
dc.title Ideals In Almost Distributive Lattice en_US
dc.type Other en_US

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