Zero-divisor graphs for modules over integral domains

Abstract

The zero-divisor graphs of modules introduced and studied in [S. Safaeeyan, M. Baziar and E. Momtahan, A generalization of the zero-divisor graph for modules, J. Korean Math. Soc. 51(1) (2014) 87–98]. Basic results for zero-divisor graphs of [Formula: see text]-modules were obtained in [M. Baziar, E. Momtahan and S. Safaeeyan, Zero-divisor graph of abelian groups, J. Algebra Appl. 13(6) (2014) 13]. In this paper, zero-divisor graphs in the title are studied. Here, among other things, we generalize results stated in [M. Baziar, E. Momtahan and S. Safaeeyan, Zero-divisor graph of abelian groups, J. Algebra Appl. 13(6) (2014) 13]. Some results for modules over non-integral domains are also obtained.