Let S be a semiring and let Z(S)∗ be its set of nonzero zero divisors. We denote the zero divisor graph of S by Γ(S) whose vertex set is Z(S)∗ and there is an edge between the vertices x and y (x 6= y) in Γ(S) if and only if either xy = 0 or yx = 0. In this paper we study the zero divisor graph of the semiring of matrices Mn(B), (n > 1) over the Boolean semiring B. We investigate the properties...

Consider the (p,q) simple connected graph . The sum absolute values of spectrum quotient matrix a make up graph's energy. objective this study is to examine energy identity graphs and zero-divisor commutative rings using group theory, applications. In study, derived from few classes ring R are examined.

Let R be a commutative ring with nonzero identity and let id="M2"> Z its set of zero divisors. The zero-divisor graph id="M3"> is the id="M4"> ? vertex id="M5"> V = ? , wh...

For a smooth scheme X of pure dimension d over field k and an effective Cartier divisor D?X whose support is simple normal crossing divisor, we construct cycle class mapcycX|D:CH0(X|D)?HNisd(X,KdM(OX,ID)) from the Chow group zero-cycles with modulus to cohomology relative Milnor K-sheaf.

In this paper, we study the genera of zero-divisor graphs with respect to ideals in finite rings.