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dc.contributor.advisorMarshall, Murrayen_US
dc.creatorWalter, Leslie J.en_US
dc.date.accessioned2012-05-25T08:38:24Zen_US
dc.date.accessioned2013-01-04T04:33:03Z
dc.date.available2013-05-25T08:00:00Zen_US
dc.date.available2013-01-04T04:33:03Z
dc.date.created1994en_US
dc.date.issued1994en_US
dc.date.submitted1994en_US
dc.identifier.urihttp://hdl.handle.net/10388/etd-05252012-083824en_US
dc.description.abstractOne obtains orders of higher level in a commutative ring A by pulling back the higher level orders in the residue fields of its prime ideals. Since inclusion relationships can hold amongst the higher level orders in a field (unlike the level 1 situation), there may exist orders in the ring A which are not contained in a unique order maximal with respect to inclusion. However, if the specializations of an order P are defined to be those orders Ǫ ⊇ P such that Ǫ P ⊆ Ǫ ∩ -Ǫ, every higher level order in A is contained in a unique maximal specialization. The real spectrum of A relative to a higher level preorder T is defined to be the set SperTA of all orders in A containing T. As with the ordinary real spectrum of Coste and Roy, SperTA is given a compact topology in which the closed points are precisely the orders in A maximal with respect to specialization. For 2-primary level, we show that an abstract higher level version of the Hormander-Šojasiewicz Inequality holds and use it to characterize the basic sets in SperTA. A higher level signature on a commutative ring A is a pull-back σ of a higher level signature on the residue field of some prime ideal þ with σ(þ) = 0. If T is a higher level preorder in A and σ(T) = {0, 1} then σ is called a T-signature. Specializations of T-signatures are defined just as for orders and every T-signature is shown to have a unique maximal specialization. Each T-signature a determines a unique order in A containing T which is maximal with respect to specialization iff σ is. Generalizing a result of M. Marshall, we show for a higher level preorder T in a commutative ring satisfying a certain simple axiom, the space XT of all maximal T-signatures can be embedded in the character group of a suitable abelian group GT of finite even exponent and under this embedding, the pair (XT, GT) is a space of signatures in the sense of Mulcahy and Marshall.en_US
dc.language.isoen_USen_US
dc.titleOrders and signatures of higher level on a commutative ringen_US
thesis.degree.departmentMathematics and Statisticsen_US
thesis.degree.disciplineMathematics and Statisticsen_US
thesis.degree.grantorUniversity of Saskatchewanen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophy (Ph.D.)en_US
dc.type.materialtexten_US
dc.type.genreThesisen_US


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