Photo by vika_strawberrika from unsplash
ABSTRACT Let R be a commutative ring with identity and let Z(R,k) be the set of all k-zero-divisors in R and k>2 an integer. The k-zero-divisor hypergraph of R, denoted… Click to show full abstract
ABSTRACT Let R be a commutative ring with identity and let Z(R,k) be the set of all k-zero-divisors in R and k>2 an integer. The k-zero-divisor hypergraph of R, denoted by âk(R), is a hypergraph with vertex set Z(R,k), and for distinct elements in Z(R,k), the set is an edge of âk(R) if and only if and the product of any (kâ1) elements of is nonzero. In this paper, we characterize all finite commutative nonlocal rings R with identity whose â3(R) has genus one.
Keywords:
genus one;
classification nonlocal;
zero divisor;
rings genus;
nonlocal rings
Journal Title: Communications in Algebra
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!
Journal Title: Communications in Algebra
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!