Geodesic
Algorithmic solvability of zero divisor recognition in a certain class of algebras
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 2, pp. 541-544.

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It is proved that the property of an element to be a one-side zero divisor is recognizable in algebras with one-side bounded conversion. 
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N. K. Ioudu. Algorithmic solvability of zero divisor recognition in a certain class of algebras. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 2, pp. 541-544. http://geodesic.mathdoc.fr/item/FPM_1995_1_2_a15/

[1] A. Ya. Belov, V. V. Borisenko, V. N. Latyshev, “Monomialnye algebry”, Algebra – 4, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 26, 2002, 35–214 | MR | Zbl

[2] V. N. Latyshev, Kombinatornaya teoriya kolets. Standartnye bazisy, Izd-vo MGU, M., 1988 | MR | Zbl