An explicit basis for the Grassmann T-space

作者：Bekh Ochir Chuluundorj; Riley David^*

来源：Journal of Algebra, 2016, 466: 63-72.

DOI：10.1016/j.jalgebra.2016.07.017

• Free algebras
• T-ideals
• T-spaces
• The Grassmann algebra

Let S-3 denote the Grassmann T-space generated by the commutator [x(1), x(2), x(3)] in the free associative algebra K < x(1), x(2),...> over a field K of characteristic zero. We construct an explicit linear basis for each KSn-module S-3 boolean AND P-n, where P-n is the space of all multilinear polynomials of degree n in indeterminates x(1),...x(n). This provides a solution to the problem of finding a linear basis for S-3, which was posed by Latyshev in circa 1990.

• 出版日期2016-11-15