Let A be a locally finitely presented Grothendieck category and let P. gl. dim A denote the
pure global dimension of A (see [12]). A is pure semisimple if P. gl. dim A= 0, or …

Professor M. Auslander has pointed out to me that the proof of [4, Theorem 2.31 is not
correct. In the present note we prove some result weaker than 14, Theorem 2.31 …

Ž. We recall that a ring R with identity is said to be of finite representation type if it is right
artinian and has only finitely many isomorphism Ž. Ž classes of finitely generated …

In representation theory as well as in other topics of ring theory it is convenient to consider
for a ring R the categories (mod R, Ab)=: D (R) and ((mod R) OP, Ab)=: L (R) of additive …

We are familiar to study rings S with identity if we are interested in homological method on
the ring theory. On the other hand, it seems for us that the theory of categories is some kind …

On splitting of module categories Page 1 Math. Z. t11, 145-150 (1969) On Splitting of Module
Categories HIROYUKI TACHIKAWA Let R be a ring and 9XR the category of all right …

Lest 6 be a locally finitely presented Grothendieck category and denote by fp (Q) the full
subcategory of 8 consisting of all finitely presented objects. We recall from [8] that (1 is pure …

An exact sequence 0--f L--+ M-+ N-+ 0 of right A-modules (where A is a ring) is called pure if
its exactness is preserved when tensoring it with any left A-module ([3]; cf. also [ZO] for …

Let C be a skeletally small abelian category with only a finite number of non-isoaorphic
simple objects and such that each object in C has finite length. Then C has a finite number of …

LetCbe a commutative artinian ring and Λ an artinC-algebra. The category of coherent
additive functorsA: mod-Λ→ Ab on the finitely presented right Λ-modules will be denoted by …