Non-commutative Zariski geometries and their classical limit

The Graded Classical Prime Spectrum with the Zariski Topology as a Notherian Topological Space

Let G be a group with identity e. Let R be a G-graded commutative ring and let M be a graded R-module. The graded classical prime spectrum Cl.Specg(M) is defined to be the set of all graded classical prime submodule of M. The Zariski topology on Cl.Specg(M); denoted by ϱg. In this paper we establish necessary and sufficient conditions for Cl.Specg(M) with the Zariski topology to be a Noetherian...

Non-commutative geometry and new stable structures

1 This paper grew out of an observation that some new stable structures discovered in the 1990' as counterexamples to well-known conjectures in pure model theory might be related to non-commutative geometry. The general meaning of the conjectures was that " very good " , or more technically, very stable structures must be in a certain way reducible to algebraic geometry over algebraically close...

Modules with Noetherian second spectrum

Let $R$ be a commutative ring and let $M$ be an $R$-module. In this article, we introduce the concept of the Zariski socles of submodules of $M$ and investigate their properties. Also we study modules with Noetherian second spectrum and obtain some related results.

Non-commutative Extensions of Classical Theories in Physics

We propose a short introductory overview of the non-commutative extensions of several classical physical theories. After a general discussion of the reasons that suggest that the non-commutativity is a major issue that will eventually lead to the unification of gravity with other fundamental interactions, we display examples of non-commutative generalizations of known geometries. Finally we dis...

Zariski-Like Topology on the Classical Prime Spectrum of a Modules