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Correction: Hesperetin prevents bone resorption by inhibiting RANKL-induced osteoclastogenesis and Jnk mediated Irf-3/c-Jun activation. [PDF]
Zhang Q +7 more
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Ilizarov gradual correction of severe post-burn bilateral knee flexion and ankle equinus contractures in an 11-year-old: a case report. [PDF]
Hidayah MRN, Calista FAK.
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Penile vascular macules: an under-recognised condition responding to pulsed dye laser. [PDF]
Madan V.
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Inhibiting the pathological changes of PASMCs is an effective approach for medicinal plants or secondary metabolites in treating pulmonary hypertension. [PDF]
Liang Q +6 more
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LEFT QUOTIENT RINGS OF ALTERNATIVE RINGS
Journal of Algebra and Its Applications, 2007In 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
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Artin’s Theorem on Alternative Rings
Mediterranean Journal of Mathematics, 2023An 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
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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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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, 1974Consider 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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