Results 11 to 20 of about 5,093 (260)
Radicals Of Polynomial Rings [PDF]
Canadian Journal of Mathematics, 1956 Introduction. Let R be a ring and let R[x] be the ring of all polynomials in a commutative indeterminate x over R. Let J(R) denote the Jacobson radical (5) of the ring R and let L(R) be the lower radical (4) of R. The main object of the present note is to determine the radicals J(R[x]) and L(R[x]).
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Simple ambiskew polynomial rings
Journal of Algebra, 2013 We determine simplicity criteria in characteristics 0 and $p$ for a ubiquitous class of iterated skew polynomial rings in two indeterminates over a base ring. One obstruction to simplicity is the possible existence of a canonical normal element $z$. In the case where this element exists we give simplicity criteria for the rings obtained by inverting $z$
Jordan, David A., Wells, Imogen E.
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An immanant formulation of the dual canonical basis of the quantum polynomial ring [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We show that dual canonical basis elements of the quantum polynomial ring in $n^2$ variables can be expressed as specializations of dual canonical basis elements of $0$-weight spaces of other quantum polynomial rings.
Mark Skandera, Justin Lambright
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A Note on Primitivity of Ideals in Skew Polynomial Rings of Automorphism Type
International Journal of Mathematics and Mathematical Sciences, 2016 We extend results about primitive ideals in polynomial rings over nil rings originally proved by Smoktunowicz (2005) for σ-primitive ideals in skew polynomial rings of automorphism type.
Edilson Soares Miranda
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Multi-Parameter Support with NTTs for NTRU and NTRU Prime on Cortex-M4
Transactions on Cryptographic Hardware and Embedded Systems, 2022 We propose NTT implementations with each supporting at least one parameter of NTRU and one parameter of NTRU Prime. Our implementations are based on size-1440, size-1536, and size-1728 convolutions without algebraic assumptions on the target polynomial ...
Erdem Alkim, Vincent Hwang, Bo-Yin Yang
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Chain conditions on composite Hurwitz series rings
Open Mathematics, 2017 In this paper, we study chain conditions on composite Hurwitz series rings and composite Hurwitz polynomial rings. More precisely, we characterize when composite Hurwitz series rings and composite Hurwitz polynomial rings are Noetherian, S-Noetherian or ...
Lim Jung Wook, Oh Dong Yeol
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Polynomial Rings over Goldie Rings
Journal of Algebra, 2001 The authors construct for each finite field \(K\) a commutative Goldie \(K\)-algebra \(R\) such that the polynomial ring \(R[X]\) is not a Goldie ring.
Antoine, Ramon, Cedó, Ferran
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α-Reflexive Rings with Involution
مجلة المختار للعلوم, 2021 This paper studies the concept of the -quasi-*-IFP (resp., -*-reflexive) *-rings, as a generalization of the quasi-*-IFP (resp., *-reflexive) *-rings and every quasi-*-IFP (resp., *-reflexive) *-ring is -quasi-*-IFP (resp., -*-reflexive).
Muna E. Abdulhafed +1 more
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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 $ $ be a derivation of $R$. We show that if $N$ is the nil radical of $R$ then $ (N)\subseteq N$ and the Jacobson radical of $R[x; ]$ is equal to $N[x; ]$. As a consequence, we have that if $R$ is locally nilpotent then $R[x; ]$ is locally nilpotent.
Bell, Jason P. +2 more
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When are the natural embeddings of classical invariant rings pure?
Forum of Mathematics, Sigma, 2023 Consider a reductive linear algebraic group G acting linearly on a polynomial ring S over an infinite field; key examples are the general linear group, the symplectic group, the orthogonal group, and the special linear group, with the classical ...
Melvin Hochster +3 more
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