Title: Some algebraic properties of generalized power series rings
Speaker: Refaat Salem (AlAzhar University, Egypt)
Abstract: In 1989, Carl Faith introduced the notion of the zero intersection property (zip) on annihilators of a ring $R$. A ring $R$ is called a right zip ring if whenever the right annihilator of a subset $X$ of $R$ vanishes, then there exists a finite subset $Y$ of $X$ such that $r_R (Y) = 0$; equivalently, for a left ideal $L$ of $R$ with $r_R (L) = 0$, there exists a finitely generated left ideal $T$ contained in $L$ such that $r_R (T) = 0$. The definition a left zip ring follows similarly.
In recent years, several algebraists have been interested in study of the zip and weak zip properties and their behavior in ring extensions. The purpose of this talk is to present the progress of work on these properties in different ring extensions, specially in skew generalized (and generalized) power series rings.