Let Γ be a coalgebra over a field k. We introduce an operator Tr that takes a right quasi-
finitely copresented Γ-comodule M to a left quasi-finitely copresented Γ-comodule Tr M. If M …

Let C be a coalgebra over an arbitrary field K. We show that the study of the category C-
Comod of left C-comodules reduces to the study of the category of (co) representations of a …

It is well known that the torsion part of any finitely generated module over the formal power
series ring K [[X]] is a direct summand. In fact, K [[X]] is an algebra dual to the divided power …

For a coalgebra (C, d, E) over a field k, there exists a natural algebra structure on its dual
space C*= Horn,(C, k) induced by the diagonal map d and the augmentation map E of C …

INTRODUCTION wx In 8, K. Morita introduced a useful notion of duality between categories
of modules, usually called ''Morita duality.''He proved that every duality is given by …

For a ring R, the properties of being (left) self-injective or being a cogenerator for the left R-
modules do not imply one another, and the two combined give rise to the important notion of …

C is a coalgebra over the field k with maps' A: C+ C@ C and E: C-jk such that (1)(1
9~)~=(A@~) A and(2)(l@ &) A=(~ 81) A= 1, mc and morphisms being C-morphisms. C*, the …

Given a K-coalgebra C and an injective left C-comodule E, we construct a coalgebra CE and
fully faithful left exact embedding□ E: CE-Comod→ C-Comod of comodule categories such …

In this paper we introduce cointegrations from one bicomodule into another, a notion
extending that of coderivation used by Nakajima [1 1] and Doi [3]. We show that in the …

Our investigation of coalgebras over commutative rings R is based on the close relationship
between comodules over a coalgebra C and modules over the dual algebra C*. If C is …