The description of varieties of rings whose finite rings are uniquely determined by their zero-divisor graphs.

Autor: Zhuravlev, E., Kuz'mina, A., Mal'tsev, Yu.
Zdroj: Russian Mathematics; Jun2013, Vol. 57 Issue 6, p10-20, 11p
Abstrakt: The zero-divisor graph of an associative ring R is defined as follows. The vertices of the graph are all the nonzero elements of the ring. Two different vertices x and y of the graph are connected by an edge if and only if xy = 0 or yx = 0. In this paper, we give the complete description of varieties of associative rings all of whose finite rings are uniquely determined by their zero-divisor graphs. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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