𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The polynomial ring over a Goldie ring need not be a Goldie ring

✍ Scribed by Jeanne Wald Kerr

Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
513 KB
Volume
134
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

πŸ“œ SIMILAR VOLUMES

Polynomial Rings over Goldie Rings
Polynomial Rings over Goldie Rings
✍ Ramon Antoine; Ferran CedΓ³ πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 99 KB

For each finite field K, we construct a commutative Goldie K-algebra R such that the polynomial ring R x is not a Goldie ring. This generalizes a construction of Kerr.

Polynomial Rings over Nil Rings Need Not
Polynomial Rings over Nil Rings Need Not Be Nil
✍ Agata Smoktunowicz πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 116 KB

We construct a nil algebra over a countable field, the polynomial ring over which is not nil. This answers a question of Amitsur.

On the Goldie Quotient Ring of the Envel
On the Goldie Quotient Ring of the Enveloping Algebra of a Classical Simple Lie Superalgebra
✍ Ian M Musson πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 100 KB

If α’„ is a classical simple Lie superalgebra α’„ / P n , the enveloping algebra Ε½ . Ε½ Ε½ .. U α’„ is a prime ring and hence has a simple artinian ring of quotients Q U α’„ by Ε½ Ε½ .. Goldie's Theorem. We show that if α’„ has Type I then Q U α’„ is a matrix ring Ε½ Ε½ .. Ε½ . over Q U α’„ . On the other hand, if α’„ s

Analogs of GrΓΆbner Bases in Polynomial R
Analogs of GrΓΆbner Bases in Polynomial Rings over a Ring
✍ LYN J. MILLER πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 617 KB

In this paper we will define analogs of GrΓΆbner bases for R-subalgebras and their ideals in a polynomial ring R[x 1 , . . . , xn] where R is a noetherian integral domain with multiplicative identity and in which we can determine ideal membership and compute syzygies. The main goal is to present and