Mathematical Sciences: Varieties of Lattices
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{'SignBlockName': 'Ann K. Boyle', 'PO_EMAI': None, 'PO_PHON': None}
This research will focus on three problems concerning the                  structure of finite algebras and finite lattices.  The first is                 to study the congruence structure of finite algebras in any                     variety of algebras satisfying a nontrivial Mal'cev condition.                  The second is to find a description of those finite length                      lattices which can be represented as a lattice of permuting                     equivalence relations.  The third is to find the lattice                        varieties covering the variety generated by a finite lattice.                        Lattices are discrete mathematical objects with a structure                reflecting to some extent the structure of set theory or logic.                 This very weak structure means that lattices can be found in many               mathematical environments.  It also means that problems are easy                to state, hard to solve and of a very general nature.  Nation has               been very successful in the past and one can expect results on                  lattices which will impact many areas of mathematics.
{'FirstName': 'James', 'LastName': 'Nation', 'PI_MID_INIT': 'B', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'James B Nation', 'EmailAddress': 'jb@math.hawaii.edu', 'NSF_ID': '000342483', 'StartDate': '06/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
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