Results 1 to 10 of about 178 (166)
Polynomial identity rings as rings of functions
Journal of Algebra, 2007 24 pages. This is the final version of the article, to appear in J. Algebra.
Zinovy Reichstein
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Differential polynomial rings over rings satisfying a polynomial identity
Journal of Algebra, 2015 Let $R$ be a ring satisfying a polynomial identity and let $δ$ be a derivation of $R$. We show that if $N$ is the nil radical of $R$ then $δ(N)\subseteq N$ and the Jacobson radical of $R[x;δ]$ is equal to $N[x;δ]$. As a consequence, we have that if $R$ is locally nilpotent then $R[x;δ]$ is locally nilpotent.
Jason P Bell, Forte Shinko
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Twisted polynomial rings satisfying a polynomial identity
Journal of Algebra, 1985 Let R be a noetherian ring with prime radical N. First, the authors investigate conditions for twisted polynomial rings over R to be FBN. They show that if R[x,\(\sigma\) ] is an FBN ring for \(\sigma\) an automorphism of R, then \({\bar \sigma}{}^ m_{Z(R/N)}=1\) for some m where \({\bar \sigma}{}_{Z(R/N)}\) is the induced automorphism of the center of
Jay Shapiro
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On the Jacobson Radical of Skew Polynomial Extensions of Rings Satisfying a Polynomial Identity [PDF]
Communications in Algebra, 2016 Let $R$ be a ring satisfying a polynomial identity and let $D$ be a derivation of $R$. We consider the Jacobson radical of the skew polynomial ring $R[x;D]$ with coefficients in $R$ and with respect to $D$, and show that $J(R[x;D])\cap R$ is a nil $D$-ideal.
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Noncommutative Prüfer Rings Satisfying a Polynomial Identity
Journal of Algebra, 1993 A prime Goldie ring \(R\) is a right Prüfer ring if for every finitely generated right \(R\)-ideal \(I\), \(I^{-1}I = R\) and \(II^{-1} = O_ l(I)\). \(R\) is a left Prüfer ring if for every finitely generated left \(R\)-ideal \(J\) of \(R\), \(JJ^{-1} = R\) and \(J^{-1}J = O_ r(R)\). \textit{J. H. Alajbegovic} and \textit{N. I. Dubrovin} [J.
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Equalizing ideal for integer-valued polynomials over the upper triangular matrix ring [PDF]
ریاضی و جامعه, 2023 Let $D$ be an integral domain and $I$ be an ideal of the upper trangular matrix ring $T_{n}(D)$. In this paper, we study the equalizing ideal$$q_{I}=\{A\in T_n(D)|f(A)-f(0)\in I,\forall f\in {\operatorname{Int}}(T_n(D))\}.$$of the integer-valued ...
Ali Reza Naghipour
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PRESIMPLIFIABLE AND WEAKLY PRESIMPLIFIABLE RINGS
Barekeng, 2023 Let be a commutative ring with identity. Two elements and b in are called to be associates if and , or equivalently, if . The generalization of associate relation in R has given the idea for definitions of presimplifiable and weakly presimplifiable
Deby Anastasya, Sri Wahyuni
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Mathematics, 2020 Let R be a commutative ring with identity, and let S be a (not necessarily saturated) multiplicative subset of R. We define R to be a nonnil-S-Noetherian ring if each nonnil ideal of R is S-finite.
Min Jae Kwon, Jung Wook Lim
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Rings with polynomial identity and centrally essential rings [PDF]
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2019 It is proved that for any prime integer $p$ and each field $F$ of characteristic $p$, there exists a centrally essential $F$-algebra which is not a PI-ring and is not algebraic over its center. Victor Markov is supported by the Russian Foundation for Basic Research, project 17-01-00895-A.
Markov, V. T., Tuganbaev, A. A.
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Composite Hurwitz Rings as PF-Rings and PP-Rings
Mathematics, 2020 Let R ⊆ T be an extension of commutative rings with identity and H ( R , T ) (respectively, h ( R , T ) ) the composite Hurwitz series ring (respectively, composite Hurwitz polynomial ring).
Dong Kyu Kim, Jung Wook Lim
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