Finitely Generated Modules Over Noncommutative Chain Rings
Type of Degreedissertation
Mathematics and Statistics
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The notion of a right chain ring, a ring whose lattice of right ideals is linearly ordered by inclusion, is a generalization of a valuation ring. In this work we investigate properties of right chain rings and the structure of modules over such rings. Several results that have been established for modules over valuation rings and domains are extended to modules over non-commutative right chain rings. In this discussion the notion of a right duo ring, a ring whose right ideals are two-sided, arises naturally.