 
Summary: Fully Coprime Comodules and Fully Coprime Corings
Jawad Y. Abuhlail
Department of Mathematical Sciences, Box # 5046
King Fahd University of Petroleum & Minerals
31261 Dhahran  Saudi Arabia
abuhlail@kfupm.edu.sa
Abstract
Prime objects were defined as generalization of simple objects in the categories
of rings (modules). In this paper we introduce and investigate what turns out to be
a suitable generalization of simple corings (simple comodules), namely fully coprime
corings (fully coprime comodules). Moreover, we consider several primeness notions
in the category of comodules of a given coring and investigate their relations with the
fully coprimeness and the simplicity of these comodules. These notions are applied
then to study primeness and coprimeness properties of a given coring, considered as
an object in its category of right (left) comodules.
1 Introduction
Prime ideals play a central role in the Theory of Rings. In particular, localization
of commutative rings at prime ideals is an essential tool in Commutative Algebra. One
goal of this paper is to introduce a suitable dual notion of coprimeness for corings over
arbitrary (not necessarily commutative) ground rings as a first step towards developing a
