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Alternative Division Rings, II
2002In this chapter we prove Theorem 17.3. Our goal is to show that the Cayley-Dickson algebras defined in (9.8) are the only non-associative alternative division rings. This result was first proved in [17] and [56] by R. Bruck and E. Kleinfeld. See also [3], [74] and [87]. In the proof we give here, the characteristic does not play any role.
Jacques Tits, Richard M. Weiss
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Generalization of alternative and commutative rings
Algebra and Logic, 1973zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Alternator ideal in weakly alternative rings
Algebra and Logic, 1993Let \(R\) be a ring which satisfies the identity \((x,y,z) = (y,z,x)\) and is without elements of orders 2 and 3 in its additive group. The author proves that \(A^ 2 = 0\), where \(A\) is the alternator ideal of \(R\). In particular, let \(R\) also be a nil ring of bounded index \(n\).
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Quasiideals in alternative rings
Acta Mathematica Hungarica, 1992The author considers (minimal) quasiideals in alternative rings. Regrettably he overlooked that his quasiideals are nothing but intersections of one-sided ideals.
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Additivity ofn-Multiplicative Maps on Alternative Rings
Communications in Algebra, 2016João CARLOS Da Motta Ferreira +1 more
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Characterization of Lie multiplicative derivation on alternative rings
Rocky Mountain Journal of Mathematics, 2019Bruno Leonardo Macedo Ferreira +1 more
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THE MAXIMAL LEFT QUOTIENT RINGS OF ALTERNATIVE RINGS
Communications in Algebra, 2005MIGUEL Gomez Lozano
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When is a Multiplicative Derivation Additive in Alternative Rings?
Communications in Algebra, 2016H Guzzo
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