Geodesic
A reduction theorem for ring varieties whose subvariety lattice is distributive
Discussiones Mathematicae. General Algebra and Applications, Tome 30 (2010) no. 1, pp. 119-132

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We prove a theorem (for arbitrary ring varieties and, in a stronger form, for varieties of associative rings) which basically reduces the problem of a description of varieties with distributive subvariety lattice to the case of algebras over a finite prime field.
Keywords: variety of rings, subvariety lattice, distributive lattice, torsion-bounded variety, Mal'tsev product 
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Volkov, Mikhail. A reduction theorem for ring varieties whose subvariety lattice is distributive. Discussiones Mathematicae. General Algebra and Applications, Tome 30 (2010) no. 1, pp. 119-132. http://geodesic.mathdoc.fr/item/DMGAA_2010_30_1_a5/