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On the radius and the relation between the total graph of a commutative ring and its extensions. (English) Zbl 1299.13010

Summary: We discuss the determination of the radius of the total graph of a commutative ring \(R\) in the case when this graph is connected. Typical extensions such as polynomial rings, formal power series, idealization of the \(R\)-module \(M\) and relations between the total graph of the ring \(R\) and its extensions are also dealt with.

MSC:

13A99 General commutative ring theory

Keywords:

zero-divisor
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