Author

Gregory Morre

Publication Date

8-25-2016

Abstract

There are numerous results regarding the cardinality of the set of star and semistar operations on a domain R. However the cardinality of the set of such operations has only just begun to be examined in the non-domain setting. Epstein has shown a correspondence between the set of finite-type semistar operations of a ring and the finite-type standard closures of a ring. I will classify the set of finite-type standard closures on several rings of dimension one.

Degree Name

Mathematics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Advisor

Vassilev, Janet

First Committee Member (Chair)

Vassilev, Janet

Second Committee Member

Buium, Alexandr

Third Committee Member

Degnan, James

Fourth Committee Member

Miller, Lance

Language

English

Keywords

closure operation, standard, semistar, weakly prime, commutative ring

Document Type

Dissertation

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