Mathematical Sciences: Topics in Commutative Ring Theory
{'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 research concerns work on the following topics in the                 area of commutative associative rings and algebras. The first is                birational normal spots and exceptional prime divisors over a 2-                dimensional normal local domain. A specific question here is                    whether a 2-dimensional normal local domain that satisfies                      Muhly's condition (N) necessarily has torsion divisor class                     group. The second topic concerns finite generation of ideals                    contracted from a polynomial ring extension. An interesting                     question in this area is whether a 1-dimensional coherent domain                has the property that its integral closure is a Prufer domain.                  The third topic concerns ring and field extensions that are not                 finitely generated but have the property that each proper                       subextension is finitely generated. Other topics in commutative                 ring theory concerned with the behavior of the Picard group under               ring extension, the structure of rings of interest in control                   theory, and the multiplicity of adjacent ideals in a 2-                         dimensional regular local domain will be considered.                                 Commutative rings are algebraic structures possessing a                    commutative addition and a commutative multiplication. These                    structures occur throughout mathematics and algebra and common                  examples include polynomial rings, and rings of algebraic                       integers in extension fields of the rationals. This project is                  concerned with a variety of questions on the structure of                       commutative rings.
{'FirstName': 'William', 'LastName': 'Heinzer', 'PI_MID_INIT': 'J', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'William J Heinzer', 'EmailAddress': 'heinzer@math.purdue.edu', 'NSF_ID': '000248749', 'StartDate': '06/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
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