The Neron-Severi group of divisor classes modulo algebraic equivalence on a smooth algebraic surface is often not difficult to calculate, and has classically been studied as one of the fundamental invariants of the surface. A more difficult problem is the determination of those divisor classes which can be represented by effective divisors; these divisor classes form a monoid contained in the N...

A divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2,... | |} V such that an edge uv is assigned the label 1 if either ( ) | ( ) f u f v or ( ) | ( ) f v f u and the label 0 if ( ) ( ) f u f v , then number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a divisor cordial labeling is called a divisor cordial ...

Elementary divisor domains were defined by Kaplansky [I. Kaplansky, Elementary divisors and modules, Trans. Amer. Math. Soc. 66 (1949) 464–491] and generalized to rings with zero-divisors by Gillman and Henriksen [L. Gillman, M. Henriksen, Some remarks about elementary divisor rings, Trans. Amer. Math. Soc. 82 (1956) 362–365]. In [M.D. Larsen, W.J. Lewis, T.S. Shores, Elementary divisor rings a...

Let G be a finite group acting faithfully on an irreducible non-singular projective curve defined over an algebraically closed field F . Does every G-invariant divisor class contain a Ginvariant divisor? The answer depends only on G and not on the curve. We answer the same question for degree 0 divisor (classes). We investigate the question for cycles on varieties.

Let $R$ be an associative ring with identity. A ring $R$ is called reversible if $ab=0$, then $ba=0$ for $a,bin R$. The quasi-zero-divisor graph of $R$, denoted by $Gamma^*(R)$ is an undirected graph with all nonzero zero-divisors of $R$ as vertex set and two distinct vertices $x$ and $y$ are adjacent if and only if there exists $0neq rin R setminus (mathrm{ann}(x) cup mathrm{ann}(y))$ such tha...

2.1 Dimension and codimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Dimension relative to a base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Cartier divisors . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

We compute all the top intersection numbers of divisors on the total space of the Poincaré bundle restricted to B × C (where B is an abelian variety, and C ⊂ B is any test curve). We use these computations to find the class of the universal theta divisor and mtheta divisor inside the universal corank 1 semiabelian variety — the boundary of the partial toroidal compactification of the moduli spa...

We study divisors in a complex manifold in view of the property that the algebra of logarithmic differential operators along the divisor is generated by logarithmic vector fields. We give • a sufficient criterion for the property, • a simple proof of F.J. Calderón–Moreno’s theorem that free divisors have the property, • a proof that divisors in dimension 3 with only isolated quasi–homogeneous s...

A divisor cordial labeling of a graph G with vertex set V vertex G is a bijection f from V to {1, 2, 3, . . . |V|} such that an edge uv is assigned the label 1 if f(u) divides f(v) or f(v)divides f(u) and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. If a graph has a divisor cordial labeling, then it is called divisor cordial gr...

We compute all the top intersection numbers of divisors on the total space of the Poincaré bundle restricted to B × C (where B is an abelian variety, and C ⊂ B is any test curve). We use these computations to find the class of the universal theta divisor and mtheta divisor inside the universal corank 1 semiabelian variety — the boundary of the partial toroidal compactification of the moduli spa...