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Right alternative rings with idempotents

✍ Scribed by Irvin Roy Hentzel


Publisher
Elsevier Science
Year
1971
Tongue
English
Weight
339 KB
Volume
17
Category
Article
ISSN
0021-8693

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πŸ“œ SIMILAR VOLUMES


Polynomial Rings over Nil Rings Cannot B
✍ K.I Beidar; Y Fong; E.R PuczyΕ‚owski πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 104 KB

We prove that the ring of polynomials in one indeterminate over a nil ring cannot be homomorphically mapped onto a ring containing a nonzero idempotent. This result can be regarded as an approximation of a positive solution of KΓΆthe's problem.

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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.