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This section describes mathematical notions and definitions used in the experimental LETTERPLACE extension of SINGULAR.

For further details, please, refer to the papers

[LL09]: Roberto La Scala and Viktor Levandovskyy, "Letterplace ideals and non-commutative Groebner bases", Journal of Symbolic Computation, Volume 44, Issue 10, October 2009, Pages 1374-1393, see http://dx.doi.org/10.1016/j.jsc.2009.03.002.

[LL13]: Roberto La Scala and Viktor Levandovskyy, "Skew polynomial rings, Groebner bases and the letterplace embedding of the free associative algebra", Journal of Symbolic Computation, Volume 48, Issue 1, January 2013, Pages 1374-1393, see http://dx.doi.org/10.1016/j.jsc.2012.05.003 and also http://arxiv.org/abs/1009.4152.

All algebras are assumed to be associative $K$-algebras for some field $K$.

7.6.1 Free associative algebras  
7.6.2 Groebner bases for two-sided ideals in free associative algebras  
7.6.3 Letterplace correspondence  
7.6.4 Example of use of LETTERPLACE  
7.6.5 Release notes of LETTERPLACE