Domestic canonical algebras and simple Lie algebras

For each simply-laced Dynkin graph $\Delta$ we realize the simple complex Lie algebra of type $\Delta$ as a quotient algebra of the complex degenerate composition Lie algebra $L(A)_{1}^{\mathbb{C}}$ of a domestic canonical algebra $A$ of type $\Delta$ by some ideal $I$ of $L(A)_{1}^{\mathbb{C}}$ that is defined via the Hall algebra of $A$, and give an explicit form of $I$. Moreover, we show that each root space of $L(A)_{1}^{\mathbb{C}}/I$ has a basis given by the coset of an indecomposable $A$-module $M$ with root easily computed by the dimension vector of $M$.Comment: 43 pages, 5 figures, revised versio

The equality I^2=QI in Buchsbaum rings

Let A be a Noetherian local ring with the maximal ideal m and d=dimA. Let Q be a parameter ideal in A. Let I=Q:m. The problem of when the equality I^2=QI holds true is explored. When A is a Cohen-Macaulay ring, this problem was completely solved by A. Corso, C. Huneke, C. Polini, and W. Vasconcelos, while nothing is known when A is not a Cohen-Macaulay ring. The present purpose is to show that within a huge class of Buchsbaum local rings A the equality I^2=QI holds true for all parameter ideals Q. The result will supply theorems of K. Yamagishi, S. Goto and K. Nishida with ample examples of ideals I, for which the Rees algebras R(I), the associated graded rings G(I), and the fiber cones F(I) are all Buchsbaum rings with certain specific graded local cohomology modules. Two examples are explored. One is to show that I^2=QI may hold true for all parameter ideals Q in A, even though A is not a generalized Cohen-Macaulay ring, and the other one is to show that the equality I^2=QI may fail to hold for some parameter ideal Q in A, even though A is a Buchsbaum local ring with multiplicity at least three.Comment: 26 pages, Rendiconti del Seminario Matematico dell'Universit di Padova (to appear

Section 337 and National Treatment under GATT: A Proposal for Legislative Reform

This Article discusses the GATT panel reports on Section 337, the U.S. reaction to the GATT findings and possible amendments to Section 337 that would put the United States in compliance with its international obligations. Taking into account the difficult balancing act necessary to change Section 337 the authors attempt to take these requirements into account in suggesting ways out of the quandary in which the United States and its trading partners now find themselves