query: Nilpotent/invertible polynomial over commutative ring.
positive_passages.docid: 150223
positive_passages.text: Nilradical and Jacobson's radical.
negative_passages.docid: 116955
negative_passages.text: Showing the existence of a certain kind of extension of a finitely generated algebra
negative_passages.docid: 112099
negative_passages.text: Polynomial ring with integral coefficients is integral
negative_passages.docid: 1425
negative_passages.text: The Chinese Remainder Theorem for Rings.
negative_passages.docid: 156443
negative_passages.text: if $x$ and $y$ commute with $[x y]$, then $[x y]$ is nilpotent
negative_passages.docid: 14873
negative_passages.text: $1+a$ and $1-a$ in a ring are invertible if $a$ is nilpotent
negative_passages.docid: 67944
negative_passages.text: Nilpotent Elements and Intersection of Prime Ideals
negative_passages.docid: 74777
negative_passages.text: Solvability and reducibility of a polynomial in a "chain" of finite fields
negative_passages.docid: 3936
negative_passages.text: Characterization of valuation rings
negative_passages.docid: 38346
negative_passages.text: Commutative Ring: Nilpotent elements closed under addition?
negative_passages.docid: 24247
negative_passages.text: Ring Inside an Algebraic Field Extension
negative_passages.docid: 77820
negative_passages.text: Roots in a polynomial ring
negative_passages.docid: 109039
negative_passages.text: Does this "extension property" for polynomial rings satisfy a universal property?
negative_passages.docid: 94174
negative_passages.text: Ring of polynomials over a field has infinitely many primes
negative_passages.docid: 108898
negative_passages.text: An Analogue of CRT for Polynomial Ring
negative_passages.docid: 145221
negative_passages.text: Ring isomorphism (polynomials in one variable)
negative_passages.docid: 89313
negative_passages.text: Maximal ideals of polynomial rings in infinitely many variables