Results 91 to 100 of about 183 (119)

On zero-divisor graphs of skew polynomial rings over non-commutative rings

Journal of Algebra and Its Applications, 2017
In this paper, we continue to study zero-divisor properties of skew polynomial rings [Formula: see text], where [Formula: see text] is an associative ring equipped with an endomorphism [Formula: see text] and an [Formula: see text]-derivation [Formula: see text].
Hashemi, E., Amirjan, R., Alhevaz, A.
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Gröbner Bases for the Modules Over Noetherian Polynomial Commutative Rings

gmj, 2008
Abstract We present the theory of Gröbner bases for the submodules of the free module 𝐴𝑚, 𝑚 ≥ 1, where 𝐴 = 𝑅[𝑥1,…,𝑥𝑛] and 𝑅 is a Noehterian commutative ring. This generalizes the theory of Gröbner bases for the ideals of 𝐴 and the submodules of (𝐾[𝑥1,…,𝑥𝑛])𝑚, where 𝐾 is a field, see [Möller, J. Symbolic Comput. 6: 345–359, 1988], [Möller,
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D-bases for polynomial ideals over commutative noetherian rings

1997
We present a completion-like procedure for constructing D-bases for polynomial ideals over commutative Noetherian rings with. unit. The procedure is described at an abstract level, by transition rules. Its termination is proved under certain assumptions about the strategy that controls the application of the transition rules. Correctness is established
Leo Bachmair, Ashish Tiwari
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Standard basis of a polynomial ideal over commutative Artinian chain ring

Discrete Mathematics and Applications, 2004
The author generalizes the notion of Gröbner basis for ideals contained in a polynomial ring \(R[x_1, \dots, x_n]\), where \(R\) is a commutative, Artinian chain ring (i.e.\ an Artinian local ring whose maximal ideal is principal). The paper follows the usual frame of Gröbner bases theory over a field and gives the corresponding notion of reduction ...
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Hopf Algebra Dual to a Polynomial Algebra over a Commutative Ring

Mathematical Notes, 2002
Over a field, the continuous dual \(A^0\) of an algebra \(A\) has several equivalent definitions, and has the structure of a coalgebra. Over a commutative ring \(R\), Artamonov has defined \(A^0\) as those \(f\) in \(A^*\) whose kernel contains an ideal \(I\) of \(A\) such that \(A/I\) is a finitely-generated projective \(R\)-module.
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On skew polynomials over Ikeda-Nakayama rings

Communications in Algebra, 2021
Abdollah Alhevaz
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On separable polynomials over a commutative ring

2016
A monic polynomial, \(f\), over the commutative ring \(R\) is separable if \(R[X]/(f)\) is a separable \(R\)-algebra. \textit{G. J. Janusz} [Trans. Am. Math. Soc. 122, 461--479 (1966; Zbl 0141.03402)] showed that if \(R\) has no non-trivial idempotents, \(f\) is separable if there is a separable, projective, \(R\)-algebra \(S\) and elements \(a_i\) of \
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Exponents of skew polynomials over periodic rings

Communications in Algebra, 2021
André Leroy
exaly  

A simple coefficient test for cubic permutation polynomials over integer rings

IEEE Communications Letters, 2006
Jonghoon Ryu
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Witt vectors with coefficients and characteristic polynomials over non-commutative rings

Compositio Mathematica, 2022
Emanuele Dotto, Irakli Patchkoria
exaly