Title page for ETD etd-042199-120414


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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