Geodesic
Standard Envelopes of Commutative Triple Systems
Matematičeskie zametki, Tome 69 (2001) no. 5, pp. 733-739

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Under certain constraints on the characteristic of a field $\Phi$, the commutative standard enveloping $q$-algebra $B$ of a commutative triple system $A$ over $\Phi$ is defined. It is proved that 1) if the algebra $B$ is simple, then the system $A$ is simple; 2) if the system $A$ is simple, then $B$ either is simple or decomposes into the direct sum of two isomorphic simple subalgebras (as of ideals). 
@article{MZM_2001_69_5_a8,
     author = {V. T. Filippov},
     title = {Standard {Envelopes} of {Commutative} {Triple} {Systems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {733--739},
     publisher = {mathdoc},
     volume = {69},
     number = {5},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_5_a8/}
}
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V. T. Filippov. Standard Envelopes of Commutative Triple Systems. Matematičeskie zametki, Tome 69 (2001) no. 5, pp. 733-739. http://geodesic.mathdoc.fr/item/MZM_2001_69_5_a8/