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Canadian Journal of Mathematics, 1952
The only known simple alternative rings which are not associative are the Cayley algebras. Every such algebra has a scalar extension which is isomorphic over its center F to the algebra where . The elements e11 and e00 are orthogonal idempotents an , for every xij of .
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The only known simple alternative rings which are not associative are the Cayley algebras. Every such algebra has a scalar extension which is isomorphic over its center F to the algebra where . The elements e11 and e00 are orthogonal idempotents an , for every xij of .
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Communications in Algebra, 1998
The right alternative law implies the left alternative law in loop rings of characteristic other than 2. We also exhibit a loop which fails to be a right Bol loop, even though its characteristic 2 loop rings are right alternative.
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The right alternative law implies the left alternative law in loop rings of characteristic other than 2. We also exhibit a loop which fails to be a right Bol loop, even though its characteristic 2 loop rings are right alternative.
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On Quotient Rings in Alternative Rings
Communications in Algebra, 2014We introduce a notion of left nonsingularity for alternative rings and prove that an alternative ring is left nonsingular if and only if every essential left ideal is dense, if and only if its maximal left quotient ring is von Neumann regular (a Johnson-like Theorem). Finally, we obtain a Gabriel-like Theorem for alternative rings.
Laura Artacho Cárdenas +2 more
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Nilpotent Ideals in Alternative Rings
Canadian Mathematical Bulletin, 1980It is well known and immediate that in an associative ring a nilpotent one-sided ideal generates a nilpotent two-sided ideal. The corresponding open question for alternative rings was raised by M. Slater [6, p. 476]. Hitherto the question has been answered only in the case of a trivial one-sided ideal J (i.e., in case J2 = 0) [5]. In this note we solve
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Prime, right alternative, almost-alternative rings
Algebra and Logic, 1986Translation from Algebra Logika 25, No.5, 600-610 (Russian) (1986; Zbl 0618.17009).
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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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Catalytic Enantioselective Ring-Opening Reactions of Cyclopropanes
Chemical Reviews, 2021Vincent Pirenne +2 more
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Intermittent fasting in the prevention and treatment of cancer
Ca-A Cancer Journal for Clinicians, 2021Katherine Clifton +2 more
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