On free partially associative triple systems
作者:
Murray Bremner,
期刊:
Communications in Algebra
(Taylor Available online 2000)
卷期:
Volume 28,
issue 4
页码: 2131-2145
ISSN:0092-7872
年代: 2000
DOI:10.1080/00927870008826948
出版商: Gordon and Breach Science Publishers Ltd.
关键词: Primary 17A40;Primary 17A50;Secondary 17-04
数据来源: Taylor
摘要:
A triple system is partially associative (by definition) if it satisfies the identity (abc)de + a(bcd)e + ab(cde) ≡ 0. This paper presents a computational study of the free partially associative triple system on one generator with coefficients in the ring Z of integers. In particular, the Z-module structure of the homogeneous submodules of (odd) degrees ≤ 11 is determined, together with explicit generators for the free and torsion components in degrees ≤ 9. Elements of additive order 2 exist in degrees ≥ 7, and elements of additive order 6 exist in degrees ≥ 9. The most difficult case (degree 11) requires finding the row-reduced form over Z of a matrix of size 364 × 273. These computations were done with Maple V.4 on a Sun workstation.
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