A Sagbi Basis for Some Subalgebras of Polynomial Rings
| dc.contributor.advisor | Tesemma, Mohammed (PhD) | |
| dc.contributor.author | Solomon, Dawit | |
| dc.date.accessioned | 2019-05-08T12:49:21Z | |
| dc.date.accessioned | 2023-11-04T12:30:49Z | |
| dc.date.available | 2019-05-08T12:49:21Z | |
| dc.date.available | 2023-11-04T12:30:49Z | |
| dc.date.issued | 2019-03-04 | |
| dc.description.abstract | A SAGBI BASIS FOR SOME SUBALGEBRAS OF POLYNOMIAL RINGS Dawit Solomon Tadesse Addis Ababa University, 2018 The term \SAGBI" is an acronym for \Subalgebra Analogue to Gr obner Bases for Ideals". There exist _nitely generated subalgebras of |[x1; x2; :::; xn] which have no _nite SAGBI basis with respect to any monomial order. There are also subalgebras which may or may not have _nite SAGBI basis depending on the monomial order de_ned on |[x1; x2; :::; xn]. We know that, there are uncountably many monomial orders de_ned on |[x1; x2; :::; xn] for n _ 2. It is still an important open problem to classify subalgebras that have a _nite SAGBI basis. In addition to this, two or more generators of a subalgebra may not form a SAGBI basis. Torstensson et al. provide su_cient and necessary conditions for two generators form a SAGBI basis, in the case of univariate polynomial ring. An other important open problem is to provide a su_cient andnor necessary condition when three or more generators form a SAGBI basis in the univariate polynomial ring as well as two or more generators form a SAGBI basis in a multivariate polynomial ring. This thesis provides su_cient conditions when two generators of a subalgebra form a SAGBI basis in a multivariate polynomial ring. We also investigate su_cient and necessary condition when generators with consecutive degrees form a SAGBI basis in the univariate polynomial ring. Finally we conjecture that subalgebras generated by two polynomials have a _nite SAGBI basis with respect to any monomial order. We prove our conjecture in certain cases. | en_US |
| dc.identifier.uri | http://etd.aau.edu.et/handle/123456789/18213 | |
| dc.language.iso | en | en_US |
| dc.publisher | Addis Ababa University | en_US |
| dc.subject | Preliminaries | en_US |
| dc.subject | Monomial Orders | en_US |
| dc.subject | Initial Algebra | en_US |
| dc.subject | Subduction | en_US |
| dc.title | A Sagbi Basis for Some Subalgebras of Polynomial Rings | en_US |
| dc.type | Thesis | en_US |