Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-20T11:33:34.710Z Has data issue: false hasContentIssue false
  • English
  • Français

Bounded and invariant elements in 2-firs

Published online by Cambridge University Press:  24 October 2008

A. J. Bowtell  and
P. M. Cohn
A. J. Bowtell
Affiliation:
Westfield College and Bedford College, University of London
P. M. Cohn
Affiliation:
Westfield College and Bedford College, University of London
Get access Rights & Permissions [Opens in a new window]

Extract

1. Introduction. In a principal ideal domain R, any two-sided ideal is of the form Rc = cR, i.e. it has an invariant element as generator, and the customary development of ideal theory in a principal ideal domain (cf. e.g. (10), ch. III) takes on a more transparent form when expressed in terms of invariant elements. Likewise, the one-sided bounded ideals may be studied in terms of their generators.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 69 , Issue 1 , January 1971 , pp. 1 - 12
Copyright
Copyright © Cambridge Philosophical Society 1971

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Amitsur, S. A.A generalization of a theorem on differential equations. Bull. Amer. Math. Soc. 54 (1948), 937–941.CrossRefGoogle Scholar
(2)Asano, K.Nichtkommutative Hauptidealringe (Paris, 1938).Google Scholar
(3)Bergman, G. M. and Cohn, P. M. The centers of 2-firs and hereditary rings (to appear).Google Scholar
(4)Carcanague, J. Anneaux de polynomes gauches (to appear.)Google Scholar
(5)Cohn, P. M.Noncommutative unique factorization domains. Trans. Amer. Math. Soc. 109 (1963), 313–331.CrossRefGoogle Scholar
(6)Cohn, P. M.Free associative algebras. Bull. London Math. Soc. 1 (1969), 1–39.CrossRefGoogle Scholar
(7)Cohn, P. M.Factorization in general rings and strictly cyclic modules. J. Reine Angew. Math. 239/240 (1970) 185–200.Google Scholar
(8)Curtis, C. W. and Reiner, I.Representation theory of finite groups and associative algebras (New York-London, 1962).Google Scholar
(9)Feller, E. H.Intersection irreducible ideals of a non-commutative principal ideal domain. Canad. J. Math. 12 (1960), 592–596.CrossRefGoogle Scholar
(10)Jacobson, N.Theory of rings (New York, 1943).Google Scholar
(11)Jacobson, N.Structure of rings (Providence, 1956, 1964).CrossRefGoogle Scholar
(12)Ore, O.Formale Theorie der linearen Differentialgleichungen. J. Reine Angew. Math. 167 (1932), 221–234, 168 (1932), 233–252.CrossRefGoogle Scholar