Type of Document	Dissertation
Author	Smith, Nathan A.
Author's Email Address	nasmith@math.vt.edu
URN	etd-042199-120414
Title	Syzygy Decompositions and Projective Resolutions
Degree	PhD
Department	Mathematics
Advisory Committee	Advisor Name Title Green, Edward L. Committee Chair Haskell, Peter E. Committee Member Linnell, Peter A. Committee Member Rossi, John F. Committee Member Thomson, James E. Committee Member
Keywords	Syzygy Resolution Algebra Module Ring Decomposition
Date of Defense	1999-04-16
Availability	restricted
Abstract We give a projective resolution of a finite dimensional K-algebra A over its enveloping algebra Ae = Aop ÄKA. The description of this resolution is related to decompositions of the first syzygy module of A as an Ae module. Resolutions of right A modules MA may be obtained by tensoring M over A with this bimodule resoution. We describe how to obtain such a resolution when M is simple or when M is given in the form of a projective presentation. Computations of ExtnA(Sv,Sw) for certain classes of algebras A are made using these resolutions, and applied to obtain results on global dimension.
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