Hostname: page-component-7b7567c8c-7pwfn Total loading time: 0 Render date: 2026-11-15T17:45:49.523Z Has data issue: false hasContentIssue false
  • English
  • Français

Separable Extensions and Centralizers of Rings

Published online by Cambridge University Press:  22 January 2016

Kazuhiko Hirata
Kazuhiko Hirata*
Affiliation:
Chiba 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.

We have introduced in [9] a type of separable extensions of a ring as a generalization of the notion of central separable algebras. Unfortunately it was unsuitable to call such extensions ‘central5 as Sugano pointed out in [15] (Example below Theorem 1.1). Some additional properties of such extensions were given in [15]. Especially Propositions 1. 3 and 1. 4 in [15] are interesting and suggested us to consider the commutor theory of separable extensions.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 35 , July 1969, pp. 31 - 45
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1969

References

[1] Auslander, M. and Goldman, O., Maximal orders, Trans. Amer. Math. Soc, 97 (1960), 1–24.CrossRefGoogle Scholar
[2] Auslander, M. and Goldman, O., The Brauer group of a commutative ring, Trans. Amer. Math. Soc, 97 (1960), 367–409.Google Scholar
[3] Azumaya, G., Completely faithful modules and self-injective rings, Nagoya Math. J., 27 (1966), 697–708.CrossRefGoogle Scholar
[4] Bass, H., The Morita theorems, Lecture note at Univ. of Oregon, 1962.Google Scholar
[5] Cartan, H. and Eilenberg, S., Homological algebra, Princeton, 1956.Google Scholar
[6] Endo, S., Completely faithful modules and quasi-Frobenius algebras, J. Math. Soc. Japan, 19 (1967), 437–456.Google Scholar
[7] Hattori, A., Semisimple algebras over a commutative ring, J. Math. Soc. Japan, 15 (1963), 404–419.Google Scholar
[8] Hirata, K. and Sugano, K., On semisimple extensions and separable extensions over non commutative rings, J. Math. Soc. Japan, 18 (1966), 360–373.CrossRefGoogle Scholar
[9] Hirata, K., Some types of separable extensions of rings, Nagoya Math. J., 33 (1968), 107–115.Google Scholar
[10] Hochschild, G., Note on relative homological algebra, Trans. Amer. Math. Soc, 82 (1956) 246–269.Google Scholar
[11] Morita, K., Duality for modules and its application to the theory of rings with minimum condition, Sci. Rep. Tokyo Kyoiku Daigaku, Sect. A, 6 (1958), 83–142.Google Scholar
[12] Morita, K., Adjoint pairs of functors and Frobenius extensions, Sci. Rep. Tokyo Kyoiku Daigaku, Sect. A, 9 (1965), 40–71.Google Scholar
[13] Müller, B., Quasi-Frobenius Erweiterungen, Math. Z., 85 (1964), 345–368.Google Scholar
[14] Müller, B., Quasi-Frobenius Erweiterungen II, Math. Z., 88 (1965), 380–409.Google Scholar
[15] Sugano, K., Note on semisimple extensions and separable extensions, Osaka J. Math., 4 (1967), 265–270.Google Scholar