query: Sum of nilpotent and element is a unit in ring?
positive_passages.docid: 22563
positive_passages.text: Units and Nilpotents
negative_passages.docid: 105887
negative_passages.text: Ring and Subring with different Identities
negative_passages.docid: 83115
negative_passages.text: A set of elements in a reduced unity ring
negative_passages.docid: 25748
negative_passages.text: If $G / Z(G)$ nilpotent then G is nilpotent.
negative_passages.docid: 69012
negative_passages.text: How to directly prove every element in a ring with exactly three ideals is either a unit or a zero divisor?
negative_passages.docid: 14343
negative_passages.text: Every nonzero element in a finite ring is either a unit or a zero divisor
negative_passages.docid: 158873
negative_passages.text: Is every group the unit group of some ring?
negative_passages.docid: 115585
negative_passages.text: Do Boolean rings always have a unit element?
negative_passages.docid: 24259
negative_passages.text: Quotient ring of $T/I$
negative_passages.docid: 154530
negative_passages.text: Rings whose elements are partitioned between units and zero-divisors.
negative_passages.docid: 21840
negative_passages.text: Zero divisors and units for the ring $\mathbb{Z}/n\mathbb{Z}$ with integer $n$
negative_passages.docid: 87946
negative_passages.text: Proving that the unities of a ring form a group under multiplication
negative_passages.docid: 20613
negative_passages.text: Units (invertibles) of polynomial rings over a field
negative_passages.docid: 50908
negative_passages.text: Showing a Ring and an Ideal are equal
negative_passages.docid: 19112
negative_passages.text: Ring $R= \mathbb Z_3[x]/\langle x^6-1\rangle$
negative_passages.docid: 92822
negative_passages.text: Finite number of elements generating the unit ideal of a commutative ring
negative_passages.docid: 133019
negative_passages.text: Nilpotent elements in $\mathbb Z_n$