Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-22T05:56:02.186Z Has data issue: false hasContentIssue false
  • English
  • Français

Hereditary Semi-Primary Rings and Tri-Angular Matrix Rings

Published online by Cambridge University Press:  22 January 2016

Manabu Harada
Manabu Harada*
Affiliation:
Osaka City University
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.

It is well known that the semi-simple rings with minimum conditions coincide with the rings of global homological dimension zero and that the hereditary rings coincide with the rings of global dimension one. Eilenberg, Jans, Nagao and Nakayama gave some properties of hereditary rings in [4] and [11], which relate to global dimension of factor rings. As an example of non-commutative hereditary ring we know a tri-angular matrix ring over a semi-simple ring.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 2 , July 1966 , pp. 463 - 484
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Auslander, M. and Goldman, O., Maximal order Trans. Amer. Math. Soc. 97 (1960), 1–24.CrossRefGoogle Scholar
[2] Chase, S. U., A generalization of the ring of triangular matrices, Nagoya Math. J. 18 (1961), 13–25.CrossRefGoogle Scholar
[3] Eilenberg, S., Homological dimension and syzgies, Ann Math. 64 (1956), 328–336.Google Scholar
[4] Eilenberg, S., Nagao, H. and Nakayama, T., On the dimension of modules and algebras, IV, Nagoya Math. J. 10 (1956), 87–96.CrossRefGoogle Scholar
[5] Harada, M., Note on the dimension of modules and algebras J. Inst. Polyt. Osaka City Univ. 7 (1956), 17–27.Google Scholar
[6] Harada, M., On homological theorems of algebras, ibid, 10 (1959), 123–127.Google Scholar
[7] Harada, M., Multiplicative ideal theory in hereditary orders, J. Math. Osaka City Univ. 14 (1963), 83–106.Google Scholar
[8] Harada, M., Structure of hereditary orders over local rings, ibid, 14 (1963), 1–22.Google Scholar
[9] Harada, M., Hereditary orders, Trans. Amer. Math. Soc. 107 (1963), 273–290.CrossRefGoogle Scholar
[10] Jacobson, N., Structure of Rings, Amer. Math. Soc. Press. (1956).Google Scholar
[11] Jans, J. P. and Nakayama, T., On the dimension of modules and algebras, VII, Nagoya Math. J. 11 (1957), 67–76.CrossRefGoogle Scholar
[12] Nagao, H. and Nakayama, T., On the structure of Mo- and Ma-modules, Math. Zeits. 59 (1953), 164–170.Google Scholar
[13] Rosenberg, A. and Zelinsky, D., Cohomology of infinite algebras, Trans. Amer. Math. Soc. 82 (1956), 85–98.CrossRefGoogle Scholar
[14] Nakano, T., A nearly semi-simple ring, Comm. Math. Univ. Sancti Pauli 7 (1959), 27–33.Google Scholar