Citation
Edmondson, D E (1954) Homomorphisms of a modular lattice. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/578R5M80. https://resolver.caltech.edu/CaltechETD:etd11212003113012
Abstract
This thesis is an algebraic study of the irreducible ideals of a modular lattice and their application to the characterization of the homomorphisms or congruence relations of the lattice.
First, an arithmetic characterization of modularity is given in terms of the irreducible ideals of the lattice. This is a new structure result for modular lattices which, since it characterizes general modular lattices, is more fundamental in the structure of modular lattices than the KuroshOre Theorem.
Second, through the arithmetic characterization developed, subsets of the irreducible ideals are used to define congruence relations on the lattice and its lattice of ideals. It is then shown that every congruence relation on a modular lattice can be so characterized.
In conclusion, a generalization of the theorem that the congruence relations of a finite dimensional modular lattice form a Boolean algebra is given by proving that the congruence relations on the lattice of ideals of a modular lattice form a Boolean algebra if and only if the lattice is finite dimensional.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Mathematics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  1 January 1954 
Record Number:  CaltechETD:etd11212003113012 
Persistent URL:  https://resolver.caltech.edu/CaltechETD:etd11212003113012 
DOI:  10.7907/578R5M80 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  4616 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  21 Nov 2003 
Last Modified:  20 Dec 2019 20:03 
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