Finding a field in a Zariski-like structure

Finding a field in a Zariski-like structure

The starting point for this dissertation is whether the concept of Zariski geometry, introduced by Hrushovski and Zilber, could be generalized to the context of nonelementary classes. This leads to the axiomatization of Zariski-like structures. As our main result, we prove that if the canonical pregeometry of a Zariski-like structure is non locally modular, then the structure interprets either ...

ZARISKI-LIKE SPACES OF CERTAIN MODULES

Let $R$ be a commutative ring with identity and $M$ be a unitary$R$-module. The primary-like spectrum $Spec_L(M)$ is thecollection of all primary-like submodules $Q$ such that $M/Q$ is aprimeful $R$-module. Here, $M$ is defined to be RSP if $rad(Q)$ isa prime submodule for all $Qin Spec_L(M)$. This class containsthe family of multiplication modules properly. The purpose of thispaper is to intro...

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

Keloid: A rare finding in Pyoderma Gangrenosum

Pyoderma gangrenosum is characterized by a chronic, non-infectious, destructive ulcer which is mostly seen on distal lower extremities, but it can be found anywhere on body. We report an 18-year old man who developed keloids after healing of his ulcers. He was a known case of chronic relapsing pyoderma gangrenosum. His previous ulcers were used to heal leaving atrophic, cigarette-paper sc...

A Note on Zariski Pairs

Definition. A couple of complex reduced projective plane curves C1 and C2 of a same degree is said to make a Zariski pair, if there exist tubular neighborhoods T (Ci) ⊂ P of Ci for i = 1, 2 such that (T (C1), C1) and (T (C2), C2) are diffeomorphic, while the pairs (P, C1) and (P , C2) are not homeomorphic; that is, the singularities of C1 and C2 are topologically equivalent, but the embeddings ...