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
For a coalgebra , the rational functor is a left exact preradical whose associated linear topology is the family , consisting of all closed and cofinite right ideals of . It was proved by Radford (1973) that if is right -Noetherian (which means that every is finitely generated), then is a radical. We show that the converse follows if , 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) is right -Noetherian; (ii) is right -Noetherian for all ; and (iii) is closed under products and is right -Noetherian. New examples of right -Noetherian coalgebras are provided.
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