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 less than or equal to 11 is determined, together with explicit generators for the free and torsion components in degrees less than or equal to 9. Elements of additive order 2 exist in degrees greater than or equal to 7, and elements of additive order 6 exist in degrees greater than or equal to 9. The most difficult case (degree 11) requires finding the row-reduced form over Z of a matrix of size 364 x 273. These computations were done with Maple V.4 on a Sun workstation. [References: 9]
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