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The Annals of Mathematics, 1953
One of the ways of gaining an insight into the nature of a class of rings is to determine all the simple ones. In the case of associative rings some restriction, such as the existence of maximal or minimal right ideals is usually made in order to characterize the simple ones, for otherwise one encounters seemingly pathological examples.
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One of the ways of gaining an insight into the nature of a class of rings is to determine all the simple ones. In the case of associative rings some restriction, such as the existence of maximal or minimal right ideals is usually made in order to characterize the simple ones, for otherwise one encounters seemingly pathological examples.
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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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Vaginal Ring an HT Alternative
The Nurse Practitioner, 2004On May 31 2002 the Womens Health Initiative (WHI) announced that the combined estrogen and progestin arm of the study was halted because the numbers of breast cancers blood clots and cardiac events exceeded the preset limits. In February 2004 the estrogen-only arm of the study was stopped as well thus ending the intervention phase of the study.
Mary M, Cothran, Sandra, Engberg
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Alternative Synthesis of Imidazobenzisothiazole Ring.
ChemInform, 2004AbstractFor Abstract see ChemInform Abstract in Full Text.
Zh. V. Shmyreva +4 more
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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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