Hostname: page-component-cb9f654ff-65tv2 Total loading time: 0 Render date: 2025-09-10T00:49:49.548Z Has data issue: false hasContentIssue false
  • English
  • Français

On Very Large One Sided Ideals of a Ring

Published online by Cambridge University Press:  20 November 2018

Kwangil Koh
Kwangil Koh*
Affiliation:
North Carolina State University Raleigh, North Carolina
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.

If R is a ring, a right (left) ideal of R is said to be large if it has non-zero intersection with each non-zero right (left) ideal of R [8]. If S is a set, let |S| be the cardinal number of S. We say a right (left) ideal I of a ring R is very large if |R/I| < < No. If a is an element of a ring R such that (a)r = {r ∊ R|ar = 0} is very large then we say a is very singular. The set of all very singular elements of a ring R is a two sided ideal of R. If R is a prime ring, then 0 is the only very singular element of R and a very large right (left) ideal of R is indeed large provided that R is not finite.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 2 , June 1966 , pp. 191 - 196
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Claude, Chevalley, Fundamental Concepts of Algebra. Academic Press, (1956).Google Scholar
2. Cartan, H. and Eilenberg, S., Homological Algebra. Princeton University Press, (1956).Google Scholar
3. Faith, C. and Utumi, Y., “Maximal Quotient Rings”, Proc. Amer. Math. Soc., vol.16, No. 5, p. 1084-1089, (1965).Google Scholar
4. Findlay, G.D. and Lambek, J., “Generalized Ring of Quotients H”, Can. Math. Bull., Vol.1, No. 3, p. 155-167, (Sept. 1958).Google Scholar
5. Hall, M., The Theory of Groups, Macmillan Co. (1959).Google Scholar
6. Jacobson, N., Lectures in Abstract Algebra, Vol.1, D. Van No strand Company, Inc., (1951).Google Scholar
7. Jacobson, N., Structure of Rings, Amer. Math. Soc. Colloquium Publ. Vol.37.Google Scholar
8. Johnson, R.E., “The Extended Centralizer of a Ring over a Module”, Proc. Amer. Math. Soc, 2, p.891-895, (1951).Google Scholar
9. Johnson, R.E., “Quotient Rings of Rings with Zero Singular Ideal”, Pacific J. of Math., Vol.11, No. 4, p. 1385-1392, (1961).Google Scholar
10. Koh, K., “A Note on a Self Injective Ring”, Can. Math. Bull, Vol.8, No.1, p. 29-32, (1965).Google Scholar