Commutative rings with genus two annihilator graphs. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Selvakumar, K.; Subajini, M.
• Is Part Of: Communications in algebra. Volume 46:Issue 1(2018)
• Page Start: 28
• Page End: 37
• Publication Date: 2018-01-02
• Subjects: Annihilator graph -- crosscap -- genus -- outerplanar -- planar; 13A15 -- 05C75; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2017.1355713
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: Let R be a commutative ring and Z ( R )* be its set of all nonzero zero-divisors. The annihilator graph of a commutative ring R is the simple undirected graph AG ( R ) with vertices Z ( R )*, and two distinct vertices x and y are adjacent if and only if ann ( xy )≠ ann ( x )∪ ann ( y ). The notion of annihilator graph has been introduced and studied by Badawi [8 ]. In this paper, we classify the finite commutative rings whose AG ( R ) are projective. Also we determine all isomorphism classes of finite commutative rings with identity whose AG ( R ) has genus two.