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Automorphism Groups of Strong Bruhat Orders of Coxeter Groups

Description: In this dissertation, we describe the automorphism groups for the strong Bruhat orders A_n-1, B_n, and D_n. In particular, the automorphism group of A_n-1 for n ≥ 3 is isomorphic to the dihedral group of order eight, D_4; the automorphism group of B_n for n ≥ 3 is isomorphic to C_2 x C_2 where C_2 is the cyclic group of order two; the automorphism group of D_n for n > 5 and n even is isomorphic to C_2 x C_2 x C_2; and the automorphism group of D_n for n ≥ 5 and n odd is isomorphic to the dihedral group D_4.
Date: August 1986
Creator: Sutherland, David C. (David Craig)

Consistency in Lattices

Description: Let L be a lattice. For x ∈ L, we say x is a consistent join-irreducible if x V y is a join-irreducible of the lattice [y,1] for all y in L. We say L is consistent if every join-irreducible of L is consistent. In this dissertation, we study the notion of consistent elements in semimodular lattices.
Date: May 1986
Creator: Race, David M. (David Michael)

Dimension Theory

Description: This paper contains a discussion of topological dimension theory. Original proofs of theorems, as well as a presentation of theorems and proofs selected from Ryszard Engelking's Dimension Theory are contained within the body of this endeavor. Preliminary notation is introduced in Chapter I. Chapter II consists of the definition of and theorems relating to the small inductive dimension function Ind. Large inductive dimension is investigated in Chapter III. Chapter IV comprises the definition of covering dimension and theorems discussing the equivalence of the different dimension functions in certain topological settings. Arguments pertaining to the dimension o f Jn are also contained in Chapter IV.
Date: August 1986
Creator: Frere, Scot M. (Scot Martin)

Some Properties of Noetherian Rings

Description: This paper is an investigation of several basic properties of noetherian rings. Chapter I gives a brief introduction, statements of definitions, and statements of theorems without proof. Some of the main results in the study of noetherian rings are proved in Chapter II. These results include proofs of the equivalence of the maximal condition, the ascending chain condition, and that every ideal is finitely generated. Some other results are that if a ring R is noetherian, then R[x] is noetherian, and that if every prime ideal of a ring R is finitely generated, then R is noetherian.
Date: May 1986
Creator: Vaughan, Stephen N. (Stephen Nick)