The aim of this paper is to establish a fuzzy version of the dualitybetween domains and completely distributive lattices. All values aretaken in a fixed frame $L$. A definition of (strongly) completelydistributive $L$-ordered sets is introduced. The main result inthis paper is that the category of fuzzy domains is dually equivalentto the category of strongly completely distributive $L$-ordereds...

the notions of quasi-prime submodules and developed  zariski topology was introduced by the present authors in cite{ah10}. in this paper we use these notions to define a scheme. for an $r$-module $m$, let $x:={qin qspec(m) mid (q:_r m)inspec(r)}$. it is proved that $(x, mathcal{o}_x)$ is a locally ringed space. we study the morphism of locally ringed spaces induced by $r$-homomorphism $mrightar...

A dually NHC-catalyzed reaction cascade comprising an initial hydroacylation of an activated ketone and subsequent Sonogashira/Heck/Suzuki coupling in the same pot is reported. The reaction mechanism and scope of the methodology is presented.

Passerini three-component reaction and multicomponent polymerization (MCP) were demonstrated to be facile methods for the preparation of photo-cleavable polymers, photo- and redox-dually cleavable polymers, as well as block copolymers.

Extending the Stone Duality Theorem, we prove two duality theorems for category ZHaus of zero-dimensional Hausdorff spaces and continuous maps. They extend also Tarski Theorem; latter is even derived from one them. We as well new EDTych extremally disconnected Tychonoff Also, describe categories which are dually equivalent to ZComp compactifications obtain a corollary Dwinger Theorem about space.