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TIFR Mathematics 2024 | Part B | Question: 16

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Let $R$ be the ring $\mathbb{C}[x] /\left(x^{2}\right)$ obtained as the quotient of the polynomial ring $\mathbb{C}[x]$ by its ideal generated by $x^{2}$. Let $R^{\times}$be the multiplicative group of units of this ring. Then there is an injective group homomorphism from $(\mathbb{Z} / 2 \mathbb{Z}) \times(\mathbb{Z} / 2 \mathbb{Z})$ into $R^{\times}$.
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Since there are only two elements in R* satisfying that g^(2)= e ,where g is in R*

are 1mod(x^2) and -1mod(x^2)
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