Polynomial Rings
On separable and \(H\)-separable polynomials in skew polynomial rings of several variables
... skew polynomial ring in which the multiplication is given by bX = Xρ(b) (b ∈ ...monic polynomial f in B[X; ρ] such that f B[X; ρ] = B [X; ρ]f is called a sepa- rable ...H-separable) polynomial if the ...
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Quasi-duo Partial skew polynomial rings
... consider rings R with a partial action α of Z on ...skew polynomial rings and partial skew Laurent polynomial rings to be quasi-duo rings and in this case we describe the ...
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Ring-LWE in Polynomial Rings
... In this work we show that by applying a different, and much simpler transformation, one can transfer the results from [LPR10] into an “easy- to-use” Ring-LWE setting (i.e. without the dual ring R ∨ ), with only a very ...
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Skew Polynomial Rings over Weak sigma-rigid Rings and sigma(*)-rings
... A non commutative analogue of associated prime ideals of a Noetherian ring has also been discussed. We would like to note that a considerable work has been done in the investiga- tion of prime ideals (in particular ...
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Automorphisms and isomorphisms of Jha Johnson semifields obtained from skew polynomial rings
... twisted polynomial f ∈ K[t; σ], where K = F q n is a finite field and σ an automorphism of K of order n, with a particular emphasis on inner automorphisms and the automorphisms of Sandler and Hughes-Kleinfeld ...
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Skew polynomial rings and overrings
... matrix rings, polynomial rings and lo calizations when the new rings are equipped with appropriate in je c t iv e ...Jordan rings is wide enough to warrant further ...
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Generalized Weyl algebras and diskew polynomial rings
... of rings (they are also called generalized Weyl algebras) that are determined by two ring endomorphisms rather than one as in the case of ‘old’ ...of rings, the diskew polynomial rings, is ...
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Polynomial Rings over Pseudovaluation Rings
... This article concerns the study of skew polynomial rings over PVDs. Let R be a ring and σ be an automorphism of R. We denote the skew polynomial ring R[x,σ ] by S(R). If I is an ideal of R such that ...
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Quiver Generalized Weyl Algebras, Skew Category Algebras and Diskew Polynomial Rings
... of rings - the diskew polynomial rings - to show that they are GWAs under a mild restriction (Theorem ...diskew polynomial rings that are GWAs satisfying the conditions of Theorem ...
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Steadiness of polynomial rings
... Obviously, any direct sum of an infinitely generated small module and non-small module is not small, however it has an infinitely generated small factor. If we look at the reason of non-steadiness of polynomial ...
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Prime Ideals and Strongly Prime Ideals of Skew Laurent Polynomial Rings
... In 14, the authors defined α-compatible rings, which are a generalization of α-rigid rings. A ring R is called α-compatible if for each a, b ∈ R, ab 0 ⇔ aαb 0. In this case, clearly the endomorphism α is ...
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Nilpotent Elements in Skew Polynomial Rings
... We extend the class of nil- ( , ) -compatible rings through various ring extensions. We show that R is a nil- ( , ) -compatible ring if and only if the ring of triangular matrix T R n is nil-( , ) ...
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The Some Properties of Skew Polynomial Rings
... We will show that skew polynomial ring has no Morita invariance by the counterexample, and the condition that skew polynomial ring has properties of Armendarizand quasi-Baer, and verify [r] ...
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Transparent Ore Extensions over Sigma-(∗)-rings
... A noncommutative analogue of associated prime ideals of a Noetherian ring has also been also discussed. We would like to note that a considerable work has been done in the investiga- tion of prime ideals (in particular ...
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The Armendariz module and its application to the Ikeda Nakayama module
... Ikeda-Nakayama modules Let S[x] and R[x] be the polynomial rings over rings S and R and, for a module S MR , let M[x] be the set of all formal polynomials in indeterminate x with coefficie[r] ...
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cuHE: A Homomorphic Encryption Accelerator Library
... over polynomial rings enabled with a number of optimizations including algebraic techniques for efficient evaluation, memory minimization techniques, memory and thread scheduling and low level CUDA ...
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Computing Hilbert Functions using the Syzygy and LCM-lattice methods
... The draw back of this sequence is that not all objects are necessarily free R-modules. Free R-modules are R-modules that are isomorphic to a direct sum of copies of R. The traditional approach (see [1]) to computing the ...
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Associated prime ideals of weak \(\sigma\)-rigid rings and their extensions
... Bhat, Associated prime ideals of skew polynomial rings, Beitrдge Algebra Geom., Vol.. Bhat, On near-pseudo-valuation rings and their extensions, Int.[r] ...
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Lie algebras of derivations with large abelian ideals
... [1] Ie.Chapovskyi, D.Efimov, A.Petravchuk, Solvable Lie algebras of derivations of polynomial rings in three variables , Applied problems of Mechanics and Mathe- matics, Lviv, issue.. Ka[r] ...
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Skew Polynomial Extensions over Zip Rings
... skew polynomial rings of automorphism type Rx; σ skew Laurent of polynomial Rx, x −1 ; σ are subrings of Rx; σ Rx, x −1 ; σ whose elements are ...
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