arXiv subjects
Publications and source records attributed to Sandra Spiroff.
We study the zero divisor graph determined by equivalence classes of zero divisors of a commutative Noetherian ring R. We demonstrate how to recover information about R from this structure. In particular, we determine how to identify associated primes from the graph.
Let f: A\to B be a ring homomorphism between Noetherian normal integral domains. We establish a general criterion for f to induce a homomorphism Cl(f): Cl(A)\to Cl(B) on divisor class groups. For instance, this criterion applies whenever f has finite flat dimension; this special case generalizes the more classical situations where f is flat or is surjective with kernel generated by an A-regular element. We extend some of Spiroff's work on the kernels of induced maps to this more general setting.
We demonstrate how some classical computations of divisor class groups can be obtained using the theory of rational coefficient Weil divisors and related results of Watanabe.
We present a purely algebraic proof of the commutativity of the operation defined by intersection with divisors on the Chow group of a local Noetherian domain.
Let A be a locally analytically unramified local ring and let J_1,...,J_k,I be ideals in A. If C=C(J_1,...,J_k;I) is the cone generated by the (k+1)-tuples (m_1,...,m_k,n) such that J_1^{m_1}...J_k^{m_k} is contained in I^n, we prove that the topological closure of C is a rational polyhedral cone. This generalizes results by Samuel, Nagata and Rees.