Right alternative rings

On local finiteness in the sense of shirshov

On rings with commutators in the nuclei

/pdf/on-rings-satisfying-a-b-c-d-0-13egrrqm1h.pdf

On rings satisfying $[(a,\,b,\,c),\,d]=0$

Generalized standard rings

Preliminaries. A ring satisfying (x, y, x) = 0 is called flexible. Trivially in flexible rings i) is satisfied and ii) reduces to (x, [y, z], w) = ([y, z], w, x). It is clear that i) and ii) hold in commutative rings. A ring satisfying (x, y, y) 0 and (y, y, x) 0 is called alternative. One easily sees that an alternative ring is flexible and satisfies ii). More generally every subring of the direct product of a family of rings satisfying i) and ii) also satisfies i) and ii). If one changes the product xy of x, y E R into yx one obtains the ring R* anti-isomorphic to R. Any one of the conditions i), ii), iii) is satisfied by a ring R if and only if it is satisfied by R*.

https://www.jstor.org/stable/pdfplus/2373446.pdf

Armin Thedy

Papers

On Rings with Completely Alternative Commutators