Answer to Question #171929 in Abstract Algebra for Sakshi Mittal

Question #171929

Cancellation law may not hold in an arbitrary ring.


1
Expert's answer
2021-03-17T07:02:38-0400

Let us show that cancellation law may not hold in an arbitrary ring. Let us consider the ring "(\\mathbb Z_8,+,\\cdot)." Then "\\overline{4}\\cdot \\overline{2}=\\overline{4}\\cdot \\overline{6}=\\overline{0}", but "\\overline{2}\\ne\\overline{6}." Therefore, cancellation law does not hold in this ring.


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