Geodesic
Finite Gr\"obner basis algebra with unsolvable problem of zero divisors
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 8, pp. 79-96.

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This work presents a sample construction of an algebra with the ideal of relations defined by a finite Gröbner basis for which the question whether this element is a zero divisor is algorithmically unsolvable. This gives the negative answer to a question raised by V. N. Latyshev. 
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I. A. Ivanov-Pogodaev. Finite Gr\"obner basis algebra with unsolvable problem of zero divisors. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 8, pp. 79-96. http://geodesic.mathdoc.fr/item/FPM_2006_12_8_a2/

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