5 Questions
According to Lemma 1.6, which of the following statements about the zero element is true?
The zero element is unique.
Based on Lemma 1.6, what can be said about the negative of an element?
The negative of an element is not unique.
From Lemma 1.6, what conclusion can be drawn about the identity element in a ring?
The identity element is unique.
According to Lemma 1.6, what happens if a ring has two different zero elements?
The two zero elements must be the same.
In the context of Lemma 1.6, what does having two different negatives for an element imply?
Having two negatives for an element violates ring properties.
This quiz covers Lemma 1.6 in Ring Theory, which proves the uniqueness of the zero element, negative of any element, and identity element in a ring. The proof for each case is provided.
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