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Added a reference to Bergman's diamond lemma
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edit approved Apr 18, 2016 at 1:16
LSpice
edit approved Apr 18, 2016 at 1:16
LSpice
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A generic argument that can be used to show that an álgebraalgebra is non-trivial is Bergman's Diamond LemmaBergman's Diamond Lemma. In this case, it immediately applies (there are no ambiguities) so for example $x$ is not in the ideal.

This method is useful even in situations in which you cannot find a representation to implement the idea in the other two answers, or when the characteristic gets in the way.

A generic argument that can be used to show that an álgebra is non-trivial is Bergman's Diamond Lemma. In this case, it immediately applies (there are no ambiguities) so for example $x$ is not in the ideal.

This method is useful even in situations in which you cannot find a representation to implement the idea in the other two answers, or when the characteristic gets in the way.

A generic argument that can be used to show that an algebra is non-trivial is Bergman's Diamond Lemma. In this case, it immediately applies (there are no ambiguities) so for example $x$ is not in the ideal.

This method is useful even in situations in which you cannot find a representation to implement the idea in the other two answers, or when the characteristic gets in the way.

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Mariano Suárez-Álvarez
Mariano Suárez-Álvarez
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A generic argument that can be used to show that an álgebra is non-trivial is Bergman's Diamond Lemma. In this case, it immediately applies (there are no ambiguities) so for example $x$ is not in the ideal.

This method is useful even in situations in which you cannot find a representation to implement the idea in the other two answers, or when the characteristic gets in the way.