On Realizing Zero-Divisor Graphs

Author: LaGrange John  

Publisher: Taylor & Francis Ltd

ISSN: 0092-7872

Source: Communications in Algebra, Vol.36, Iss.12, 2008-12, pp. : 4509-4520

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Abstract

An algorithm is presented for constructing the zero-divisor graph of a direct product of integral domains. Moreover, graphs which are realizable as zero-divisor graphs of direct products of integral domains are classified, as well as those of Boolean rings. In particular, graphs which are realizable as zero-divisor graphs of finite reduced commutative rings are classified.