Results 241 to 250 of about 459,763 (289)

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   +1 more
openaire   +1 more source

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   +2 more
openaire   +1 more source

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
openaire   +2 more sources

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
openaire   +1 more source

Home - About - Disclaimer - Privacy