In this paper, we study the transfer of some $t$-locally properties which are stable under localization to $t$-flat overrings an integral domain $D$. We show that $D,$ $D[X],$ $D\langle X\rangle,$ $D(X)$ and $D[X]_{N_v}$ simultaneously P$v$MDs (resp., Krull, G-GCD, Noetherian, Strong Mori). A complete characterization when a pullback is P$v$MD GCD, Mori, Mori) given. As corollaries, investigate...

We develop a notion of a generalized Cuntz-Krieger family of projections and partial isometries where the range of the partial isometries need not have trivial intersection. We associate to these generalized Cuntz-Krieger families a directed graph, with a coloring function on the edge set. We call such a directed graph an edge-colored directed graph. We then study the C∗algebras and the non-sel...

and x y denotes the product x ‘3~ = my + y.2’. In Section 1 we show that a noncommutative Jordan algebra of characteristic # 2 must satisfy (1). Since power-associative algebras satisfying (1) need not be flexible [5] it follows that the class of power-associative algebras satisfying (1) is strictly larger than the class of noncommutative Jordan algebras. In Section 2 we obtain a structure theo...

These lectures given in Montreal in Summer 1997 are mainly based on, and form a condensed survey of the book by N. Chriss and V. Ginzburg, Representation Theory and Complex Geometry , Birkhäuser 1997. Various algebras arising naturally in Representation Theory such as the group algebra of a Weyl group, the universal enveloping algebra of a complex semisimple Lie algebra, a quantum group or the ...