[PDF][PDF] Pure semisimple categories and rings of finite representation type

D Simson - Journal of Algebra, 1977 - core.ac.uk
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 …

[PDF][PDF] Pure semisimple categories and rings of finite representation type

D Simson - Journal of Algebra, 1980 - core.ac.uk
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 …

[PDF][PDF] Additive categories of locally finite representation type

NV Dung, JL Garcı́a - Journal of Algebra, 2001 - core.ac.uk
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 …

[PDF][PDF] On the global dimension of the functor category ((mod R) op, Ab) and a theorem of Kulikov

H Brune - Journal of Pure and Applied Algebra, 1983 - library.navoiy-uni.uz
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 …

Perfect categories. II. Hereditary categories

M Harada - 1973 - projecteuclid.org
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 …

[引用][C] On splitting of module categories

H Tachikawa - Mathematische Zeitschrift, 1969 - Springer
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 …

[PDF][PDF] On the structure of locally finite pure semisimple Grothendieck categories

D Simson - Cahiers de topologie et géométrie différentielle, 1982 - numdam.org
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 …

[PDF][PDF] Purity in functor categories

B Stenström - Journal of Algebra, 1968 - core.ac.uk
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 …

Representation theory of artin algebras II

M Auslander - Communications in algebra, 1974 - Taylor & Francis
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 …

The endomorphism ring of a localized coherent functor

I Herzog - Journal of Algebra, 1997 - Elsevier
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 …