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Algebra and Discrete Mathematics, 2013, Volume 16, Issue 2, Pages 160–170
(Mi adm444)
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RESEARCH ARTICLE
A maximal T-space of F3[x]0
C. Bekh-Ochir, S. Rankin Department of Mathematics, University of Western Ontario, London, Ontario, Canada N6A 5B7
Abstract:
In earlier work, we have established that for any finite field k, the free associative k-algebra on one generator x, denoted by k[x]0, has infinitely many maximal T-spaces, but exactly two maximal T-ideals (each of which is a maximal T-space). However, aside from these two T-ideals, no specific examples of maximal T-spaces of k[x]0 were determined at that time. In a subsequent work, we proposed that for a finite field k of characteristic p>2 and order q, for each positive integer n which is a power of 2, the T-space Wn, generated by {x+xqn,xqn+1}, is maximal, and we proved that W1 is maximal. In this note, we prove that for q=p=3, W2 is maximal.
Received: 24.04.2012 Revised: 20.05.2012
Citation:
C. Bekh-Ochir, S. Rankin, “A maximal T-space of F3[x]0”, Algebra Discrete Math., 16:2 (2013), 160–170
Linking options:
https://www.mathnet.ru/eng/adm444 https://www.mathnet.ru/eng/adm/v16/i2/p160
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Abstract page: | 212 | Full-text PDF : | 105 | References: | 54 |
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