Article
Licensed
Unlicensed
Requires Authentication
On the algebras of almost minimal rank
-
V. V. Lysikov
Published/Copyright:
June 22, 2013
Abstract
We consider the bilinear complexity of multiplication in local and semisimple algebras over an infinite field of characteristic differing from 2. We obtain a criterion for the rank of a local algebra to be almost minimal. We evaluate the bilinear complexity of the algebras of generalised quaternions over such a field; we prove that any simple algebra of almost minimal rank is an algebra of generalised quaternions. This result is used for the classification of semisimple algebras of almost minimal rank.
Published Online: 2013-06-22
Published in Print: 2012-10
© 2013 by Walter de Gruyter GmbH & Co.
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- Masthead
- On the algebras of almost minimal rank
- Definition of positively closed classes by endomorphism semigroups
- The power conjugacy search problem in a cyclic subgroup in groups with the condition C.3/ & T.6/
- Lawvere intervals and the Möbius function of a Möbius category
- On algorithmic solvability of the A-completeness problem for systems of boundedly determinate functions containing all one-place boundedly determinate S-functions
- On uniqueness of alphabetic decoding
- On unstable branching graphs
- Extremal sets of graphs in the problem of demarcation in the family of hereditary closed classes of graphs
- Statistical problems on random permutations with censored data
- On large deviations of branching processes in a random environment with arbitrary initial number of particles: critical and supercritical cases
- Multitype branching processes evolving in a Markovian environment
- On solutions and algebraic duality of generalised linear discrete time systems
- On the number of Gram’s intervals containing the ordinates of successive zeros of the Riemann zeta function
Articles in the same Issue
- Masthead
- On the algebras of almost minimal rank
- Definition of positively closed classes by endomorphism semigroups
- The power conjugacy search problem in a cyclic subgroup in groups with the condition C.3/ & T.6/
- Lawvere intervals and the Möbius function of a Möbius category
- On algorithmic solvability of the A-completeness problem for systems of boundedly determinate functions containing all one-place boundedly determinate S-functions
- On uniqueness of alphabetic decoding
- On unstable branching graphs
- Extremal sets of graphs in the problem of demarcation in the family of hereditary closed classes of graphs
- Statistical problems on random permutations with censored data
- On large deviations of branching processes in a random environment with arbitrary initial number of particles: critical and supercritical cases
- Multitype branching processes evolving in a Markovian environment
- On solutions and algebraic duality of generalised linear discrete time systems
- On the number of Gram’s intervals containing the ordinates of successive zeros of the Riemann zeta function
