Abstract
UDC 519.17 Let R be a commutative ring with identity, which is not an integral domain. An ideal I of a ring R is called an annihilating ideal if there exists r ∈ R - { 0 } such that I r = ( 0 ) . The total graph of non-zero annihilating ideals of R , denoted by Ω ( R ) , is а graph with the vertex set A ( R ) * , the set of all non-zero annihilating ideals of R , and two distinct vertices I and J are joined if and only if I + J is also an annihilating ideal of R . We study the forcing metric dimension of Ω ( R ) and determine the forcing metric dimension of Ω ( R ) . It is shown that the forcing metric dimension of Ω ( R ) is equal either to zero or to the metric dimension.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
