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Rings in which every infinite subset contains a pair of elements with zero product
Citation
Gardner, BJ, Rings in which every infinite subset contains a pair of elements with zero product, Mathematica Pannonica, 23, (1) pp. 125-134. ISSN 0865-2090 (2012) [Refereed Article]
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Copyright Statement
Copyright 2012 Mathematica Pannonica
Official URL: http://ttk.pte.hu/mii/html/pannonica/index.htm
Abstract
B. H. Neumann has shown that every infinite subset of a group
G contains a pair of commuting elements if and only if G is finite modulo its centre. Here we consider, analogously, the rings in which each infinite subset contains distinct elements x, y with xy = 0 = yx. We show that the rings in question are those which are finite modulo their annihilators provided that they also satisfy the identity x2 ≈ 0, which many (and perhaps all) do.
Item Details
| Item Type: | Refereed Article |
|---|---|
| Keywords: | Ring, infinite subset, zero product. |
| Research Division: | Mathematical Sciences |
| Research Group: | Pure Mathematics |
| Research Field: | Operator Algebras and Functional Analysis |
| Objective Division: | Expanding Knowledge |
| Objective Group: | Expanding Knowledge |
| Objective Field: | Expanding Knowledge in the Mathematical Sciences |
| UTAS Author: | Gardner, BJ (Dr Barry Gardner) |
| ID Code: | 83553 |
| Year Published: | 2012 |
| Deposited By: | Mathematics and Physics |
| Deposited On: | 2013-03-18 |
| Last Modified: | 2017-11-01 |
| Downloads: | 1 View Download Statistics |
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