Sandra Spiroff

A Zero Divisor Graph Determined by Equivalence Classes of Zero Divisors

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.

Progress in Commutative Algebra 2 : Closures, Finiteness and Factorization

This article is a survey of closure operations on ideals in commutative rings, with an emphasis on structural properties and on using tools from one part of the field to analyze structures in another part. The survey is broad enough to encompass the radical, tight closure, integral closure, basically full closure, saturation with respect to a fixed ideal, and the v-operation, among others.

MAPS ON DIVISOR CLASS GROUPS INDUCED BY RING HOMOMORPHISMS OF FINITE FLAT DIMENSION

Let ϕ : A → B be a ring homomorphism between Noetherian normal integral domains. We estab- lish a general criterion for ϕ to induce a homomorphism Cl(ϕ ):C l(A) → Cl(B) on divisor class groups. For instance, this criterion applies whenever ϕ has finite flat dimension; this special case generalizes the more classical situations where ϕ is flat or is surjective with kernel generated by an A-regular element. We extend some of Spiroffs work on the kernels of induced maps to this more general setting.

Torsion in kernels of induced maps on divisor class groups

We investigate torsion elements in the kernel of the map on divisor class groups of excellent local normal domains A and A/I, for an ideal I of finite projective dimension. The motivation for this work is a result of Griffith-Weston which applies when I is principal.