Results 251 to 260 of about 1,152,813 (297)

LEFT QUOTIENT RINGS OF ALTERNATIVE RINGS

Journal of Algebra and Its Applications, 2007
In this paper we develop a Fountain–Gould-like Goldie theory for alternative rings. We characterize alternative rings which are Fountain–Gould left orders in semiprime alternative rings coinciding with their socle, and those which are Fountain–Gould left orders in semiprime artinian alternative rings.
Gómez Lozano, Miguel, Siles Molina, Mercedes   +1 more
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Artin’s Theorem on Alternative Rings

Mediterranean Journal of Mathematics, 2023
An alternative ring is a ring \(A\) that satisfies the identities \((xx)y = x(xy)\) and \(y(xx) = (yx)x\). A division ring is a ring with 1 such that each nonzero element has a multiplicative inverse. This paper extends some well known theorems to alternative division rings.
Ferreira, Bruno Leonardo Macedo, Barreiro, Elisabete, de Araujo Smigly, Douglas   +2 more
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Alternative loop rings

Publicationes Mathematicae Debrecen, 2022
Let R be a commutative and associative ring without elements of additive order 2. Let L be a loop. The following conditions are equivalent: (i) The loop ring RL is alternative. (ii) If x,y,\(z\in L\) are such that \(x.yz=xy.z\) then \(a.bc=ab.c\) whenever \(\{a,b,c\}=\{x,y,z\}\) and if \(x.yz\neq xy.z\) then \(xy.z=x.zy=y.xz.\) (iii) L is an extra loop
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Generalizing alternative rings

Communications in Algebra, 1974
Consider a ring R that satisfies the identity (x, x, x) 0 and any two of the three identities: (wx, y, z) + (w, x, [y, z]) w(x, y, z) (w, y, z)x = 0; ([w, x],,y, z) + (w, x, yz) y(w, x, z) (w, x, y)z = 0; (w, x y, z) x (w, y, z) y * (w, x, z) = 0. In this paper, we prove that if R has characteristic prime to 6 then R semiprime with idempotent e implies
Seyoum Getu, D.J. Rodabaugh
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Simple Alternative Rings

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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Alternative Division Rings, II

2002
In 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, 2004
On 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, 2004
AbstractFor Abstract see ChemInform Abstract in Full Text.
Zh. V. Shmyreva, L. F. Ponomareva, T. V. Zemtsova, V. V. Frolova, Yu. N. Titova   +4 more
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