This book is intended for graduate students and research mathematicians interested in associative rings and algebras, and noncommutative geometry.

Let $\mathcal N$ and $\mathcal M$ be von Neumann algebras. It is proved that $L DEGREESp(\mathcal N)$ does not linearly topologically embed in $L DEGREESp(\math

This book provides a comprehensive introduction to the interactions between noncommutative algebra and classical algebraic geometry.

In this paper we prove Lusztig's conjecture on based ring for an affine Weyl group of type $\tilde A_{n-1}$.

Generalizes the Le cycles and numbers to the case of hyper surfaces inside arbitrary analytic spaces. This book defines the Le-Vogel cycles and numbers, and pro