query: Determine the units of the ring $A= \mathbb Z[X]/(X^3)$ and the structure of the group $A^*$
positive_passages.docid: 148550
positive_passages.text: Units in quotient ring of $\mathbb Z[X]$
negative_passages.docid: 20097
negative_passages.text: Cardinality of the quotient ring $\mathbb{Z}[x]/(x^2-3,2x+4)$
negative_passages.docid: 11000
negative_passages.text: Fundamental group of $\mathbb{R}^2 \setminus (\mathbb{Z} \times \{0\})$
negative_passages.docid: 140557
negative_passages.text: Counting ring homomorphisms from $\mathbb{Z}[x,y]/(x^3+y^2-1)$ to $\mathbb{Z_7}$
negative_passages.docid: 24259
negative_passages.text: Quotient ring of $T/I$
negative_passages.docid: 158873
negative_passages.text: Is every group the unit group of some ring?
negative_passages.docid: 73743
negative_passages.text: Number of elements in the quotient ring $\mathbb{Z}[X]/(X^2-3, 2X+4)$
negative_passages.docid: 137201
negative_passages.text: Classifying $\mathbb{Z} \times \mathbb{Z} \times \mathbb{Z} / \langle(3,3,3)\rangle$
negative_passages.docid: 18361
negative_passages.text: Does the unit generate the additive group in a unital ring with cyclic additive group?
negative_passages.docid: 107821
negative_passages.text: The ring of integers of $\mathbf{Q}[i]$
negative_passages.docid: 127814
negative_passages.text: Number of elements in the quotient ring $\mathbb{Z}_6 [x]/\langle 2x +4\rangle$
negative_passages.docid: 12524
negative_passages.text: Galois group of $x^3 - 2 $ over $\mathbb Q$
negative_passages.docid: 35691
negative_passages.text: $\mathbb Z[\sqrt 3]$ contains infinitely many units
negative_passages.docid: 93703
negative_passages.text: Groups of units of $\mathbb{Z}\left[\frac{1+\sqrt{-3}}{2}\right]$
negative_passages.docid: 2235
negative_passages.text: Showing $\text{Aut}_\mathsf{Grp}(\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}) \cong S_3$
negative_passages.docid: 61391
negative_passages.text: Which finite groups are the group of units of some ring?
negative_passages.docid: 118911
negative_passages.text: Classifying Unital Commutative Rings of Order $p^2$