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Full-Text Articles in Algebra
On Conjectures Concerning Nonassociate Factorizations, Jason A Laska
On Conjectures Concerning Nonassociate Factorizations, Jason A Laska
Doctoral Dissertations
We consider and solve some open conjectures on the asymptotic behavior of the number of different numbers of the nonassociate factorizations of prescribed minimal length for specific finite factorization domains. The asymptotic behavior will be classified for Cohen-Kaplansky domains in Chapter 1 and for domains of the form R=K+XF[X] for finite fields K and F in Chapter 2. A corollary of the main result in Chapter 3 will determine the asymptotic behavior for Krull domains with finite divisor class group.
Elasticity Of Krull Domains With Infinite Divisor Class Group, Benjamin Ryan Lynch
Elasticity Of Krull Domains With Infinite Divisor Class Group, Benjamin Ryan Lynch
Doctoral Dissertations
The elasticity of a Krull domain R is equivalent to the elasticity of the block monoid B(G,S), where G is the divisor class group of R and S is the set of elements of G containing a height-one prime ideal of R. Therefore the elasticity of R can by studied using the divisor class group. In this dissertation, we will study infinite divisor class groups to determine the elasticity of the associated Krull domain. The results will focus on the divisor class groups Z, Z(p infinity), Q, and general infinite groups. For the groups Z and Z(p infinity), it has …