IJPAM: Volume 26, No. 4 (2006)


Abhishek Banerjee
Department of Mathematics
Johns Hopkins University
404 Krieger Hall, 3400 North Charles Street
Baltimore, MD 21218-2686, USA
e-mail: abhishek_banerjee1313@yahoo.co.in

Abstract.In this paper, we define the notion of an essential factor extension of a Noetherian integral domain and obtain a characterization of unique factorization domains in terms of the non existence of ``proper essential factor extensions''. The inspiration for this comes from the rather unrelated fact that a module is injective if and only if it has no proper essential extensions. Following this, we define a generalization of this notion to subrings of a given ring and consider separately the rings which are essential factor extensions of all those subrings which are `large enough', in the sense that we consider only those subrings $R$ of $S$ which are such that $S \subseteq K(R)$. Following this, we also obtain the basic properties of essential factor extensions.

Received: October 12, 2005

AMS Subject Classification: 13F15

Key Words and Phrases: unique factorization domains, essential factor extensions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 26
Issue: 4