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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 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
Author:Gardner, BJ (Dr Barry Gardner)
ID Code:83553
Year Published:2012
Deposited By:Mathematics and Physics
Deposited On:2013-03-18
Last Modified:2013-07-23
Downloads:1 View Download Statistics

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