International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 505429 | https://doi.org/10.1155/S0161171203203471

J. Cuadra, "Extensions of rational modules", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 505429, 9 pages, 2003. https://doi.org/10.1155/S0161171203203471

Extensions of rational modules

Received30 Mar 2002

Abstract

For a coalgebra C, the rational functor Rat():CC is a left exact preradical whose associated linear topology is the family C, consisting of all closed and cofinite right ideals of C. It was proved by Radford (1973) that if C is right -Noetherian (which means that every IC is finitely generated), then Rat() is a radical. We show that the converse follows if C1, the second term of the coradical filtration, is right -Noetherian. This is a consequence of our main result on -Noetherian coalgebras which states that the following assertions are equivalent: (i) C is right -Noetherian; (ii) Cn is right -Noetherian for all n; and (iii) C is closed under products and C1 is right -Noetherian. New examples of right -Noetherian coalgebras are provided.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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