Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-28T08:24:28.709Z Has data issue: false hasContentIssue false
  • English
  • Français

Systems that are Purely Simple and Pure Injegtive

Published online by Cambridge University Press:  20 November 2018

Frank Okoh
Frank Okoh*
Affiliation:
University of Nigeria, Nsukka, Nigeria
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

There has been a lot of progress made on the finite-dimensional representations of species. In [3] and [11] the finite-dimensional representations of tame species are classified and in [13] it is shown that if S is a species of finite type, then every representation of 5 is a direct sum of finite-dimensional ones. However, comparatively little is known about infinite-dimensional representations.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 4 , 01 August 1977 , pp. 696 - 700
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Aronszajn, N. and Fixman, U., Algebraic spectral problems, Studia Math 30 (1968), 273–338.Google Scholar
2. Brenner, S. and Ringel, C. M., Pathological modules over tame rings, to appear.Google Scholar
3. Dlab, V. and Ringel, C. M., Representations of graphs and algebras, Mem. Amer. Math. Soc. 173 (1976).Google Scholar
4. Fixman, U., On algebraic equivalence between pairs of linear transformations, Trans. Amer. Math. Soc. 113 (1964), 424–453.Google Scholar
5. Fixman, U. and Okoh, F., Extensions of pairs of linear transformations between infinitedimensional vector spaces, to appear, Linear Algebra and Its Applications.Google Scholar
6. Fixman, U. and Zorzitto, F., A purity criterion for pairs of linear transformations, Can. J. Math. 26 (1973), 734–745.Google Scholar
7. Fuchs, L., Infinite abelian groups, Vol. 1 (Academic Press, 1970).Google Scholar
8. Maclane, S., Homology (Springer Verlag, New York, 1967).Google Scholar
9. Okoh, F., A bound on the rank of purely simple systems, to appear, Trans. Amer. Math. Soc.Google Scholar
10. Okoh, F. Torsion-free modules over a non-commutative hereditary ring, Ph.D. thesis, Queen's University Kingston, Ontario, 1975.Google Scholar
11. Ringel, C. M., Representations of K-species and bimodules, J. Algebra 11 (1976), 269–302.Google Scholar
12. Ringel, C. M. Unions of chains of indecomposable modules. Comm. in Algebra 3 (12) (1975), 1121–1144.Google Scholar
13. Ringel, C. M. and Tachikawa, H., QF-3 rings, J. Reine Ang. Math. 272 (1975), 49–72.Google Scholar
14. Walker, C. P., Relative homologuai algebra and abelian groups, Illinois J. Math. 10 (1966), 186–209.Google Scholar