Geodesic
Additivity of elementary maps on alternative rings
Algebra and discrete mathematics, Tome 28 (2019) no. 1, pp. 94-106

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Let $\mathfrak{R}$ and $\mathfrak{R}'$ be alternative rings. In this article we investigate the additivity of surjective elementary maps of ${\mathfrak{R}\times \mathfrak{R}'}$. As a main theorem, we prove that if $\mathfrak{R}$ contains a non-trivial idempotent satisfying some conditions, these maps are additive.
Keywords: elementary maps, alternative rings, additivity. 
@article{ADM_2019_28_1_a6,
     author = {B. L. M. Ferreira},
     title = {Additivity of elementary maps on alternative rings},
     journal = {Algebra and discrete mathematics},
     pages = {94--106},
     publisher = {mathdoc},
     volume = {28},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2019_28_1_a6/}
}
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B. L. M. Ferreira. Additivity of elementary maps on alternative rings. Algebra and discrete mathematics, Tome 28 (2019) no. 1, pp. 94-106. http://geodesic.mathdoc.fr/item/ADM_2019_28_1_a6/