Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T21:50:49.588Z Has data issue: false hasContentIssue false

On the commutativity of some class of rings

Published online by Cambridge University Press:  09 April 2009

Abdullah Harmanci
Affiliation:
Department of Mathematics Hacettepe University, Ankara, Turkey.
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.

Throughout, R will denote an associative ring with center Z. For elements x, y of R and k a positive integer, we define inductively [x, y]0 = x, [x, y] = [x, y]1 = xyyx, [x, y, y, hellip, y]k = [[x, y, y, hellip, y]k−1, y]. A ring R is said to satisfy the k-th Engel condition if [x, y, y, hellip, y]k = 0. By an integral domain we mean a nonzero ring without nontrivial zero divisors.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1976

References

Amitsur, S. A. (1957), ‘A generalisation of Hilsert's nullstellensatz’, Proc. Amer. Math. Soc. 8, 649656.Google Scholar
Amitsur, S. A. (1955), ‘On rings with identities’, J. London Math. Soc. 30, 464470.CrossRefGoogle Scholar
Herstein, I. N. (1962), ‘Sugli Anelli Soddis, ad una Cond. di Engel’, Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 32, 177180.Google Scholar
Herstein, I. N. (1968), ‘Non-commutative’, New York.Google Scholar
Herstein, I. N. (1969), ‘Topics in ring theory’, Chicago.Google Scholar
Koc, M. Ikeda-C. (1974), ‘On the commutator ideal of certain rings’, Arc. der Math. 25, 348353.Google Scholar
Jacobson, N. (1964), ‘Structure of Rings’, Amer. Math. Soc. Coll. Publ.Google Scholar
Kaplansky, I. (1948), ‘Rings with a polynomial identity’, Bull. Amer. Math. Soc. 54, 575580.CrossRefGoogle Scholar
McCoy, N. H. (1964), ‘The Theory of Rings’, MacMillan.Google Scholar