Syzygy Decompositions and Projective Resolutions
| dc.contributor.author | Smith, Nathan A. | en |
| dc.contributor.committeechair | Green, Edward L. | en |
| dc.contributor.committeemember | Haskell, Peter E. | en |
| dc.contributor.committeemember | Linnell, Peter A. | en |
| dc.contributor.committeemember | Rossi, John F. | en |
| dc.contributor.committeemember | Thomson, James E. | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2014-03-14T21:10:34Z | en |
| dc.date.adate | 1999-04-24 | en |
| dc.date.available | 2014-03-14T21:10:34Z | en |
| dc.date.issued | 1999-04-16 | en |
| dc.date.rdate | 2000-04-24 | en |
| dc.date.sdate | 1999-04-21 | en |
| dc.description.abstract | We give a projective resolution of a finite dimensional 𝛫-algebra 𝛬 over its enveloping algebra 𝛬<SUP>𝑒</SUP> = 𝛬<SUP>𝑜𝑝</SUP> ⨂<SUB>𝛫</SUB>𝛬. The description of this resolution is related to decompositions of the first syzygy module of 𝛬 as an 𝛬<SUP>𝑒</SUP> module. Resolutions of right 𝛬 modules 𝑀<SUB>𝛬</SUB> may be obtained by tensoring 𝑀 over 𝛬 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 <I>𝐸𝑥𝑡</I><SUB>𝛬</SUB><SUP>𝑛</SUP>(𝑆<SUB>𝑣</SUB>,𝑆<SUB>𝑤</SUB>) for certain classes of algebras 𝛬 are made using these resolutions, and applied to obtain results on global dimension. | en |
| dc.description.degree | Ph. D. | en |
| dc.identifier.other | etd-042199-120414 | en |
| dc.identifier.sourceurl | http://scholar.lib.vt.edu/theses/available/etd-042199-120414/ | en |
| dc.identifier.uri | http://hdl.handle.net/10919/37649 | en |
| dc.publisher | Virginia Tech | en |
| dc.relation.haspart | etd.pdf | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject | Syzygy | en |
| dc.subject | Resolution | en |
| dc.subject | Algebra | en |
| dc.subject | Module | en |
| dc.subject | Ring | en |
| dc.subject | Decomposition | en |
| dc.title | Syzygy Decompositions and Projective Resolutions | en |
| dc.type | Dissertation | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | doctoral | en |
| thesis.degree.name | Ph. D. | en |
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