Graduation date: 1967This paper is the record of an exploration of two quadratic\ud number fields. The first section is devoted to the field with elements\ud of the form a +b√3 where a and b are rational numbers.\ud This field contains an integral domain in which unique factorization\ud holds. The second section is concerned with a field having an integral\ud domain in which the unique factorization theorem does not hold;\ud therefore ideals are introduced to restore this property. The\ud elements of this field are of the form a +b √-l5 where a and b\ud are rational numbers
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