I will discuss some aspects of the treatment of finiteness in its various facets given in (1) in the nontransformational theories of Head-Driven Phrase Structure Grammar (HPSG) and Lexical-Functional Grammar (LFG).1 Due to the way that syntactic information is represented in these approaches, it can be stated at the outset that finiteness is considered to really be a property of a clause. From ...

This note investigate some finiteness properties of the category U of unstable modules. One shows finiteness properties for the injective resolution of finitely generated unstable modules. One also shows a stabilization result under Frobenius twist for Ext-groups.

A bstract Brane configurations in a circle allow subsequent applications of the Hanany-Witten transitions, which are known as duality cascades. By studying process cascades corresponding to quantum curves with symmetries Weyl groups, we find hidden structure affine groups. Namely, fundamental domain consisting all final destinations is characterized by chamber and realized translations group, w...

The controlled finiteness obstruction and torsion are defined using controlled algebra, giving a more algebraic proof of the topological invariance of torsion and the homotopy finiteness of compact ANRs.

In this paper we use "ring changed'' Gorenstein homologicaldimensions to define Cohen-Macaulay injective, projective and flatdimensions. For doing this we use the amalgamated duplication of thebase ring with semi-dualizing ideals. Among other results, we prove that finiteness of these new dimensions characterizes Cohen-Macaulay rings with dualizing ideals.