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On Commutativity and Centrality in Infinite Rings |
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| Authors: | A Abdollahi H E Bell A A Klein |
| Institution: | 1. Department of Mathematics , University of Isfahan , Isfahan, Iran a.abdollahi@math.ui.ac.ir;3. Department of Mathematics , Brock University , St. Catharines, Ontario, Canada;4. School of Mathematical Sciences , Tel Aviv University , Ramat Aviv, Tel Aviv, Israel |
| Abstract: | We show that if R is an infinite ring such that XY ∩ YX ≠ ? for all infinite subsets X and Y, then R is commutative. We also prove that in an infinite ring R, an element a ∈ R is central if and only if aX ∩ Xa ≠ ? for all infinite subsets X. |
| Keywords: | Commutativity conditions Conditions for belonging to the center Infinite rings |