Hostname: page-component-848d4c4894-nmvwc Total loading time: 0 Render date: 2024-07-04T06:28:21.515Z Has data issue: false hasContentIssue false
  • English
  • Français

Regular Rank Rings

Published online by Cambridge University Press:  20 November 2018

Israel Halperin
Israel Halperin*
Affiliation:
Queen's 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.

1.1. Throughout this note, will denote an associative ring but we shall not require to possess a unit.

If A and B are subsets of , then A + B will denote the set {x + y| x ∊ A, y ∊ B}. Aτ will denote the set {u ∊ | au = 0 for all a ∊ A} .

Elements a and b will be said to be orthogonal if ab = ba = 0.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 709 - 719
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Alexander, J. H., Approximately finite geometries and their coordinate rings, University of Tennessee, Ph.D. Dissertation (1957), unpublished.Google Scholar
2. Fryer, K. D. and Israel Halperin, Coordinates in geometry, Trans. Roy. Soc. Can., Sect. III, 48 (1954), 11–26.Google Scholar
3. Fryer, K. D. and Israel Halperin, The von Neumann coordinatization theorem for complemented modular lattices, Acta Sci. Math. Szeged., 17 (1956), 203–249.Google Scholar
4. von Neumann, J., Continuous geometry (Princeton, 1960).Google Scholar
5. von Neumann, J., Examples of continuous geometries, Proc. Nat. Acad. Sci. U.S.A., 22 (1936), 101–108.Google Scholar
6. von Neumann, J., Independence of Foefrom the sequence v (Reviewed by I. Halperin), Collected Works, Vol. IV, 189–190 (New York, 1962).Google Scholar
7. von Neumann, J., The non-isomorphism of certain continuous rings, Ann. of Math., 67 (1958), 485–496.Google Scholar