Two Remarks On The Commutativity Of Rings

I. N. Herstein

doi:10.4153/CJM-1955-044-2

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In (1) and (2) we proved that under certain conditions a given ring R must be commutative. The conditions used there were “global” in the sense that they were imposed at once on the relation of a given element to all the other elements of the ring R.

References

1. Herstein., I. N. “A Theorem on Rings,” Can. J. Math., 5 (1953), 238–241.Google Scholar

2. Herstein., I. N., “A Generalization of a Theorem of Jacobson III,” Amer. J. Math., 75 (1953), 105–111.Google Scholar

3. Herstein., I. N., “The Structure of a Certain Class of Rings,” Amer. J. Math., 75 (1953), 864–871.Google Scholar

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Drazin, M. P. 1957. Rings with nil commutator ideals. Rendiconti del Circolo Matematico di Palermo, Vol. 6, Issue. 1, p. 51.

Faith, Carl 1961. Radical extensions of rings. Proceedings of the American Mathematical Society, Vol. 12, Issue. 2, p. 274.

Herstein, I. N. 1975. On a Result of Faith. Canadian Mathematical Bulletin, Vol. 18, Issue. 4, p. 609.

Herstein, I.N 1975. On the hypercenter of a ring. Journal of Algebra, Vol. 36, Issue. 1, p. 151.

Harmanci, A. 1977. Two elementary commutativity theorems for rings. Acta Mathematica Academiae Scientiarum Hungaricae, Vol. 29, Issue. 1-2, p. 23.

Gupta, V. 1980. Some remarks on the commutativity of rings. Acta Mathematica Academiae Scientiarum Hungaricae, Vol. 36, Issue. 3-4, p. 233.

Hirano, Yasuyuki and Tominaga, Hisao 1981. Some commutativity theorems for rings. Hiroshima Mathematical Journal, Vol. 11, Issue. 3,

Nada, Itzhak 1986. On a centre-like subset of a ring without nil ideals. Bulletin of the Australian Mathematical Society, Vol. 34, Issue. 1, p. 149.

Klein, A. A. and Nada, I. 1986. A commutativity result for rings. Bulletin of the Australian Mathematical Society, Vol. 33, Issue. 3, p. 359.

Bell, Howard E. and Nada, Itzhak 1987. On some center-like subsets of rings. Archiv der Mathematik, Vol. 48, Issue. 5, p. 381.

Bell, Howard E. 1990. A Criterion for Commutativity of Rings. Results in Mathematics, Vol. 18, Issue. 3-4, p. 197.

Komatsu, Hiroaki and Tominaga, Hisao 1991. Some Commutativity Conditions for Rings with Unity. Results in Mathematics, Vol. 19, Issue. 1-2, p. 83.

Ashraf, M. and Quadri, M. A. 1993. Some conditions for the commutativity of rings. Acta Mathematica Hungarica, Vol. 61, Issue. 1-2, p. 73.

Bell, Howard E. 1994. ON PSEUDO-COMMUTATMTY AND COMMUTATIVITY IN RINGS. Quaestiones Mathematicae, Vol. 17, Issue. 2, p. 173.

Gonçalves, Jairo Z. and Mandel, Arnaldo 1996. A commutativity theorem for division rings and an extension of a result of Faith. Results in Mathematics, Vol. 30, Issue. 3-4, p. 302.

Bell, Howard E. 2000. Commutativity of Rings with Constraints on Commutators, II. Results in Mathematics, Vol. 38, Issue. 1-2, p. 1.

Khan, Moharram A. 2000. Commutativity of rings through a Streb's result. Czechoslovak Mathematical Journal, Vol. 50, Issue. 4, p. 791.

Khan, Moharram A. 2002. Commutativity of rings with polynomial constraints. Czechoslovak Mathematical Journal, Vol. 52, Issue. 2, p. 401.

Pinter-Lucke, James 2007. Commutativity conditions for rings: 1950–2005. Expositiones Mathematicae, Vol. 25, Issue. 2, p. 165.

Khan, Moharram 2010. A Commutativity Study for Certain Rings. Annals of the Alexandru Ioan Cuza University - Mathematics, Vol. 56, Issue. 1,

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