Idealizer Rings and Noncommutative Projective Geometry

We study some properties of graded idealizer rings with an emphasis on applications to the theory of noncommutative projective geometry. In particular we give examples of rings for which the $\chi$-conditions of Artin and Zhang and the strong noetherian property have very different behavior on the left and right sides.Comment: 17 Pages, revised version: significant changes--introduction rewritten, new section on tensor products added, main theorem restated at en

Generic Noncommutative Surfaces

We study a class of noncommutative surfaces and their higher dimensional analogues which provide answers to several open questions in noncommutative projective geometry. Specifically, we give the first known graded algebras which are noetherian but not strongly noetherian, answering a question of Artin, Small, and Zhang. In addition, these examples are maximal orders and satisfy the $\chi_1$ condition but not $\chi_i$ for $i \geq 2$, answering a questions of Stafford and Zhang and a question of Stafford and Van den Bergh. Finally, we show that these algebras have finite cohomological dimension.Comment: 43 pages, Latex, to appear in Advances in Math. Result on finite global dimension added, other minor change

Innovativeness of the US economy. Permanent or weakening dominance?

The paper is divided into three parts. In the first one, main causes of American leadership in the field of technology are explained. In the second part, innovation performance of the US economy in comparison with the EU and Asian economies is presented. Finally, there is an analysis of innovation capacity of US economy in the context of challenges resulting from the financial and economic crisis.Strukturę opracowania można przedstawić następująco: po wprowadzeniu dokonano charakterystyki głównych czynników i procesów, które przyczyniły się do powstania dominacji gospodarki Stanów Zjednoczonych w dziedzinie innowacyjności, następnie poddano analizie zjawisko zmniejszania się przewagi innowacyjnej tej gospodarki nad resztą świata, a w dalszej kolejności skoncentrowano uwagę na zagadnieniu wpływu współczesnego kryzysu gospodarczego na perspektywy utrzymania przewagi technologicznej Stanów Zjednoczonych