Semi-simplicity of alternative loop rings
β Scribed by E. G. Goodaire; M. M. Parmenter
- Publisher
- Akadmiai Kiad
- Year
- 1987
- Tongue
- English
- Weight
- 396 KB
- Volume
- 50
- Category
- Article
- ISSN
- 1588-2632
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π SIMILAR VOLUMES
Let L be an RA loop, that is, a loop whose loop ring in any characteristic is an alternative, but not associative, ring. We find necessary and sufficient conditions Ε½ . for the Moufang unit loop of RL to be solvable when R is the ring of rational integers or an arbitrary field.
Commutative differentially simple rings have proved to be quite useful as a source of examples in noncommutative algebra. In this paper we use the theory of holomorphic foliations to construct new families of derivations with respect to which the polynomial ring over a field of characteristic zero i