Mathematical Sciences: Rings and Groups
{'Code': '03040300', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ann K. Boyle', 'PO_EMAI': None, 'PO_PHON': None}
This project concerns three problems in algebra. The first                 involves groups acting on affine domains and the resulting                      dynamics for prime ideals. The new notion of variant ideal will                 play a central role. Second, the principal investigator will                    study the stable module theory of algebras with a Lazard                        p-filtration, with the intent of settling the zero divisor                      problem for subgroups of integer matrix groups. Finally an                      abstract theory of groups with norms and expanding                              endomorphisms will be developed.                                                     The theory of groups arose in the last century as a tool                   for studying operations that can be done and undone. They have                  proved to be extremely useful in all mathematical fields                        including algebra, analysis and topology. Linear algebra arose                  in the last century also, as a way of describing high                           dimensional spaces and as a method of solving many equations in                 many variables. This project in the theory of group rings                       combines these two threads of modern algebra.
{'FirstName': 'Daniel', 'LastName': 'Farkas', 'PI_MID_INIT': 'R', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Daniel R Farkas', 'EmailAddress': None, 'NSF_ID': '000317113', 'StartDate': '05/15/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Virginia Polytechnic Institute and State University', 'CityName': 'BLACKSBURG', 'ZipCode': '240603359', 'PhoneNumber': '5402315281', 'StreetAddress': '300 TURNER ST NW', 'StreetAddress2': 'STE 4200', 'CountryName': 'United States', 'StateName': 'Virginia', 'StateCode': 'VA', 'CONGRESSDISTRICT': '09', 'CONGRESS_DISTRICT_ORG': 'VA09', 'ORG_UEI_NUM': 'QDE5UHE5XD16', 'ORG_LGL_BUS_NAME': 'VIRGINIA POLYTECHNIC INSTITUTE & STATE UNIVERSITY', 'ORG_PRNT_UEI_NUM': 'M515A1DKXAN8'}
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{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8821754.xml'}