We introduce the notion of strong test module and show that a large number of such modules appear in the tight closure theory of complete domains: the test ideal (this has already been known), the parameter test module, and the module of relative test elements. They also appear as certain multiplier ideals, a concept of interest in algebraic geometry.

Mucosal repair is a complex event that immediately follows acute injury induced by ischemia and noxious luminal contents such as bile. In the small intestine, villous contraction is the initial phase of repair and is initiated by myofibroblasts that reside immediately beneath the epithelial basement membrane. Subsequent events include crawling of healthy epithelium adjacent to the wound, referr...

We construct normal hypersurfaces whose local cohomology modules have infinitely many associated primes. These include unique factorization domains of characteristic zero with rational singularities, as well as F-regular unique factorization domains of positive characteristic. As a consequence, we answer a question on the associated primes of Frobenius powers of ideals, which arose from the loc...

Hochster and Huneke proved in [HH6] fine behaviors of symbolic powers of ideals in regular rings, using the theory of tight closure. In this paper, we use generalized test ideals, which are a characteristic p analogue of multiplier ideals, to give a slight generalization of Hochster-Huneke's results.

Maintenance of spindle attachment to the cortex and formation of the cleavage furrow around the protruded spindle are essential for polar body extrusion (PBE) during meiotic maturation of oocytes. Although spindle movement to the cortex has been well-studied, how the spindle is maintained at the cortex during PBE is unknown. Here, we show that activation of Diaphanous-related formin mediated by...

Simplified Mechanisms with an Application to Sponsored-Search Auctions Paul Milgrom First draft: August 16, 2007 This draft: December 17, 2008 A mechanism can be simplified by restricting its message space. If the restricted message spaces satisfy a certain “outcome closure property,” then the simplification is “tight”: for every , any Nash equilibrium of the simplified mechanism is also an Nas...

We are interested in the state complexity of languages that are defined via the subword closure operation. The subword closure of a set S of fixed-length words is the set of all words w for which any subword of w of the fixed length is in S. This type of constraint appears to be useful in various situations related to data encodings and in particular to DNA encodings. We present a few results r...

Let R be an excellent Noetherian ring of prime characteristic. Consider an arbitrary nested pair of ideals (or more generally, a nested pair of submodules of a fixed finite module). We do not assume that their quotient has finite length. In this paper, we develop various sufficient numerical criteria for when the tight closures of these ideals (or submodules) match. For some of the criteria we ...