Details:
Title  On Linear Equations in Some NonCommutative Algebras  Author(s)  Jonas Mansson  Type  Technical Report, Misc  Abstract  The problem of solving linear equations in a noncommutative algebra is in general a highly nontrivial matter. Even in the case of finitely presented algebras, there is no general algorithms for solving seemingly simple equations of the type a X = X b for some elements a and b.
In this paper we will demonstrate a method by which it is possible to find all the solutions to linear equations in certain factor algebras of the noncommutative polynomial ring. The commutative case reduces to computing syzygy modules, which is treated in Adams [1]. Here we will consider algebras the center of which is sufficiently large, in the sense that the former can be considered a Noetherian module over a subalgebra of its center. We will show that with the aid of Groebner
basis technique, the problem of finding the solutions in the noncommutative setting can be reduced to computing a syzygy module.  Length  8 
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 Language  English  Year  1999  Edition  0  Translation 
No  Refereed 
No 
