𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Composition Algebras over Rings of Fractions Revisited

✍ Scribed by S Pumplün

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
232 KB
Volume
201
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

Let k be a field of characteristic not two, let f x , x gk x , x be an h 0 1 0 1 irreducible homogeneous polynomial and denote the ring of elements of degree w x w x zero in the homogeneous localization k x , x by k x , x . For deg f s 3 it 0 1 f 0 1 Žf . h h h w x is proved that the composition algebras over k x , x not containing zero 0 1 Žf . h Ž . divisors are defined over k and that there is at most one split composition algebra w x not defined over k. For deg f s 4 all composition algebras over k x , x are h 0 1 Žf . h enumerated and partly classified.

📜 SIMILAR VOLUMES

Composition Algebras over a Ring of Frac
Composition Algebras over a Ring of Fractions
✍ S. Pumplün 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 242 KB

Using some theorems on composition algebras over rings of genus zero and elementary results from algebraic geometry, all composition algebras over a ring of fractions related to the projective line over a field are enumerated and partly classified.

“Modules of Finite Rank over Prüfer Ring
“Modules of Finite Rank over Prüfer Rings” Revisited
✍ Isidore Fleischer 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 114 KB

Conditions for a finite rank module over an almost maximal valuation domain to be a direct sum of uniserials are developed.

The Ring of Fractions of a Jordan Algebr
The Ring of Fractions of a Jordan Algebra
✍ C Martı́nez 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 128 KB

We derive a necessary and sufficient Ore type condition for a Jordan algebra to have a ring of fractions.

Automorphisms of Certain Lie Algebras of
Automorphisms of Certain Lie Algebras of Upper Triangular Matrices over a Commutative Ring
✍ You'an Cao 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 187 KB

Let R be an arbitrary commutative ring with identity. Denote by t the Lie algebra over R consisting of all upper triangular n by n matrices over R and let b be the Lie subalgebra of t consisting of all matrices of trace 0. The aim of this paper is to give an explicit description of the automorphism