Left and right Gröbner bases in Ore extensions of polynomial rings:
Abstract: "We show, that Gröbner bases can be computed for left and right ideals of certain Ore extensions of polynomial rings. Consider an Ore extension K[X₁, ..., X[subscript m]][Y;[alpha], [delta]] of a polynomial ring over a field, where [formula] for some f[subscript i] [element of] K[X₁ ....
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Passau
1996
|
| Schriftenreihe: | Universität <Passau> / Fakultät für Mathematik und Informatik: MIP
1996,01 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "We show, that Gröbner bases can be computed for left and right ideals of certain Ore extensions of polynomial rings. Consider an Ore extension K[X₁, ..., X[subscript m]][Y;[alpha], [delta]] of a polynomial ring over a field, where [formula] for some f[subscript i] [element of] K[X₁ ..., X[subscript m]], f[subscript i]<X[subscript i][superscript ei] for some admissible term order <, e[subscript i] [element of] N[0] and [alpha][line]K = id. This rings are in general neither right nor left Noetherian. Nevertheless finite left and right Gröbner bases for finitely generated left and right ideals do exist for special term orders. Using this Gröbner bases the ideal membership problem can be solved. For other term orders no finite Gröbner bases exist in general. Finite left and right Gröbner bases can be computed using left/right reduction and s- polynomials (based on right/left divisibility and left/right least common multiples) in Buchbergers algorithm. Termination can be proven by a modified Dickson lemma, using the special term order." |
| Beschreibung: | 28, 4 S. |
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| 520 | 3 | |a Abstract: "We show, that Gröbner bases can be computed for left and right ideals of certain Ore extensions of polynomial rings. Consider an Ore extension K[X₁, ..., X[subscript m]][Y;[alpha], [delta]] of a polynomial ring over a field, where [formula] for some f[subscript i] [element of] K[X₁ ..., X[subscript m]], f[subscript i]<X[subscript i][superscript ei] for some admissible term order <, e[subscript i] [element of] N[0] and [alpha][line]K = id. This rings are in general neither right nor left Noetherian. Nevertheless finite left and right Gröbner bases for finitely generated left and right ideals do exist for special term orders. Using this Gröbner bases the ideal membership problem can be solved. For other term orders no finite Gröbner bases exist in general. Finite left and right Gröbner bases can be computed using left/right reduction and s- polynomials (based on right/left divisibility and left/right least common multiples) in Buchbergers algorithm. Termination can be proven by a modified Dickson lemma, using the special term order." | |
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| id | DE-604.BV010678654 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-10T17:04:59Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007126954 |
| oclc_num | 36067061 |
| open_access_boolean | |
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| owner_facet | DE-154 DE-739 DE-12 DE-91G DE-BY-TUM DE-384 DE-634 |
| physical | 28, 4 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| record_format | marc |
| series2 | Universität <Passau> / Fakultät für Mathematik und Informatik: MIP |
| spelling | Pesch, Michael Verfasser aut Left and right Gröbner bases in Ore extensions of polynomial rings Michael Pesch Passau 1996 28, 4 S. txt rdacontent n rdamedia nc rdacarrier Universität <Passau> / Fakultät für Mathematik und Informatik: MIP 1996,01 Abstract: "We show, that Gröbner bases can be computed for left and right ideals of certain Ore extensions of polynomial rings. Consider an Ore extension K[X₁, ..., X[subscript m]][Y;[alpha], [delta]] of a polynomial ring over a field, where [formula] for some f[subscript i] [element of] K[X₁ ..., X[subscript m]], f[subscript i]<X[subscript i][superscript ei] for some admissible term order <, e[subscript i] [element of] N[0] and [alpha][line]K = id. This rings are in general neither right nor left Noetherian. Nevertheless finite left and right Gröbner bases for finitely generated left and right ideals do exist for special term orders. Using this Gröbner bases the ideal membership problem can be solved. For other term orders no finite Gröbner bases exist in general. Finite left and right Gröbner bases can be computed using left/right reduction and s- polynomials (based on right/left divisibility and left/right least common multiples) in Buchbergers algorithm. Termination can be proven by a modified Dickson lemma, using the special term order." Gröbner bases Polynomial rings Theoretische Informatik (DE-588)4196735-5 gnd rswk-swf Informatik (DE-588)4026894-9 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Theoretische Informatik (DE-588)4196735-5 s Informatik (DE-588)4026894-9 s Mathematik (DE-588)4037944-9 s DE-604 Fakultät für Mathematik und Informatik: MIP Universität <Passau> 1996,01 (DE-604)BV000905393 1996,01 |
| spellingShingle | Pesch, Michael Left and right Gröbner bases in Ore extensions of polynomial rings Gröbner bases Polynomial rings Theoretische Informatik (DE-588)4196735-5 gnd Informatik (DE-588)4026894-9 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4196735-5 (DE-588)4026894-9 (DE-588)4037944-9 |
| title | Left and right Gröbner bases in Ore extensions of polynomial rings |
| title_auth | Left and right Gröbner bases in Ore extensions of polynomial rings |
| title_exact_search | Left and right Gröbner bases in Ore extensions of polynomial rings |
| title_full | Left and right Gröbner bases in Ore extensions of polynomial rings Michael Pesch |
| title_fullStr | Left and right Gröbner bases in Ore extensions of polynomial rings Michael Pesch |
| title_full_unstemmed | Left and right Gröbner bases in Ore extensions of polynomial rings Michael Pesch |
| title_short | Left and right Gröbner bases in Ore extensions of polynomial rings |
| title_sort | left and right grobner bases in ore extensions of polynomial rings |
| topic | Gröbner bases Polynomial rings Theoretische Informatik (DE-588)4196735-5 gnd Informatik (DE-588)4026894-9 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Gröbner bases Polynomial rings Theoretische Informatik Informatik Mathematik |
| volume_link | (DE-604)BV000905393 |
| work_keys_str_mv | AT peschmichael leftandrightgrobnerbasesinoreextensionsofpolynomialrings |