Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-01-27T12:35:43.596Z Has data issue: false hasContentIssue false
  • English
  • Français

Equivalent Conditions for a Ring to Be a Multiplication Ring

Published online by Cambridge University Press:  20 November 2018

Joe Leonard Mott
Joe Leonard Mott*
Affiliation:
Louisiana State University Baton Rouge, Louisiana
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.

In this paper a ring will always mean a commutative ring with identity element. Furthermore, a ring R is called a multiplication ring if, whenever A and B are ideals of R and A is contained in B, there is an ideal C such that A = BC. Noetherian multiplication rings have been studied by Asano (1), Krull (4, 5), and Mori (6, 7). Krull also studied non-Noetherian multiplication rings (3). In (8, 9), Mori studied non-Noetherian multiplication rings which did not necessarily contain an identity element.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 429 - 434
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Asano, Keizo, Über kommutative Ringe, in denen jedes Ideal als Produkt von Primidealen darstellbar ist, J. Math. Soc. Japan, 1 (1951), 82–90.Google Scholar
2. Krull, Wolfgang, Idealtheorie in Ringen ohne Endlichkeitsbedingung, Math. Ann., 29 (1928), 729–744.Google Scholar
3. Krull, Wolfgang, Über allgemeine Multiplikationsringe, Tohoku Math. J., 41 (1936), 320–326.Google Scholar
4. Krull, Wolfgang, Über den Aufbau des Nullideals in ganz abgeschlossenen Ringen mit Teilerkettensatz, Math. Ann., 102 (1926), 363–369.Google Scholar
5. Krull, Wolfgang, Uber Multiplikations ringe, Sitzber. Heidelberg. Akad. Wiss. Abhandl. 5 (1925), 13–18.Google Scholar
6. Mori, Shinziro, Allgemeine Z.P.I. Ringe, J. Sci. Hiroshima Univ., Ser. A, 10 (1940), 117- 136. jm Axiomatische Begrùndung des Multiplikationsringes, J. Sci. Hiroshima Univ., Ser. A, 3 (1932), 45–59.Google Scholar
8. Mori, Shinziro, Über allgemeine Multiplikationsringe I, J. Sci. Hiroshima Univ., Ser. A, 4 (1934), 1–26.Google Scholar
9. Mori, Shinziro, Über allgemeine Multiplikationsringe II, J. Sci. Hiroshima Univ., Ser. A, 4 (1934), 33–109.Google Scholar
10. Zariski, O. and Samuel, P., Commutative algebra, vol. I (New York, 1958).Google Scholar