No CrossRef data available.
Article contents
Some results on finiteness of radical algebras
Published online by Cambridge University Press: 09 April 2009
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.
R denotes always a radical algebra over a field φ. A left ring ideal of R which is also a subvector space over φ is called a left algebra ideal of R. R is said to be left algebra noetherian if it satisfies the ascending chain condition for left algebra ideals. If dim R < ∞, then (i) R is finitely generated (ii) R is left alehra noetherian (iii) R is algebraic. Since the radical of an algebraic algebra is nil ([4] P. 19), conditions (i), (ii), (iii) are also sufficient for R to be finite-dimensional.
- Type
- Research Article
- Information
- Copyright
- Copyright © Australian Mathematical Society 1970
References
[1]Amitsur, S., ‘A generalization of Hilbert's Nullstellensatz’, Proc. Amer. Math. Soc. 8 (1957) 649–656.Google Scholar
[2]Golod, E. C., ‘On nil algebras and finitely approximable p-groups’, Izv. Akad. Nauk SSSR. Math. Ser. 28 (1964) 273–276.Google Scholar
[3]Herstein, I. N., Theory of rings (Chicago Univ. Mathematics lecture notes, 1961) 23–25.Google Scholar
[4]Jacobson, N., Structure of rings (Amer. Math. Soc. Colloquium Publications, vol. 37, 1956).Google Scholar
[5]Johnson, R. E., ‘Principal right ideal rings’, Canadian J. Math. 15 (1963), 297–301.CrossRefGoogle Scholar
You have
Access