Results 11 to 20 of about 183 (119)

STABLY CO-TAME POLYNOMIAL AUTOMORPHISMS OVER COMMUTATIVE RINGS [PDF]

Transformation Groups, 2017
We say that a polynomial automorphism $ $ in $n$ variables is stably co-tame if the tame subgroup in $n$ variables is contained in the subgroup generated by $ $ and affine automorphisms in $n+1$ variables. In this paper, we give conditions for stably co-tameness of polynomial automorphisms.
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Nilpotents and units in skew polynomial rings over commutative rings [PDF]

Journal of the Australian Mathematical Society, 1979
AbstractLet R be a commutative ring with an automorphism ∞ of finite order n. An element f of the skew polynomial ring R[x, α] is nilpotent if and only if all coefficients of fn are nilpotent. (The case n = 1 is the well-known description of the nilpotent elements of the ordinary polynomial ring R[x].) A characterization of the units in R[x, α] is also
Rimmer, M., Pearson, K. R.
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Prime factor rings of skew polynomial rings over a commutative Dedekind domain

Rocky Mountain Journal of Mathematics, 2012
Let \(D\) be a commutative Dedekind domain, \(\sigma\) an automorphism of \(D\) with the quotient field \(K\), and \(R=D[x;\sigma]\) the skew polynomial ring over \(D\). Let \(\text{Spec}(R)\) be the set of prime ideals of \(R\) and \(\text{Spec}_0(R)=\{P\in\text{Spec}(R)\mid P\cap D=(0)\}\).
Wang, Y., Amir, A.K., Marubayashi, H.
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Authentication Schemes Using Polynomials Over Non-Commutative Rings [PDF]

International Journal on Cryptography and Information Security, 2012
Authentication is a process by which an entity,which could be a person or intended computer,establishes its identity to another entity.In private and public computer networks including the Internet,authentication is commonly done through the use of logon passwords.
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Nilpotent graphs of skew polynomial rings over non-commutative rings

Transactions on Combinatorics, 2019
Summary: Let \(R\) be a ring and \(\alpha\) be a ring endomorphism of \(R\). The undirected nilpotent graph of \(R\), denoted by \(\Gamma_N(R)\), is a graph with vertex set \(Z_N(R)^*\), and two distinct vertices \(x\) and \(y\) are connected by an edge if and only if \(xy\) is nilpotent, where \(Z_N(R)=\{x\ \in R\, |\, xy \text{ is nilpotent, for some
Mohammad Javad Nikmehr, Abdolreza Azadi
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Zero estimates for polynomials over commutative rings

Mathematische Annalen, 1985
The zero estimates in question are lower bounds for the degree of polynomials, over a commutative Noetherian ring R, which vanish on initial segments of a finitely generated subgroup \(\Gamma\) of the additive group \((R^+)^ n\) or the multiplicative semigroup \((R^{\times})^ n\).
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Polynomial functions and permutation polynomials over some finite commutative rings

Journal of Number Theory, 2004
The author considers rings of integers over \(p\)-adic fields to obtain results on permutation polynomials. Some involve simplifications of the proofs of classical results, while others involve new interpretations of permutation polynomials in terms of Witt polynomials, for instance.
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Lattice of ideals of the polynomial ring over a commutative chain ring [PDF]

Applicable Algebra in Engineering, Communication and Computing, 2015
Let $R$ be a commutative chain ring. We use a variation of Gr bner bases to study the lattice of ideals of $R[x]$. Let $I$ be a proper ideal of $R[x]$. We are interested in the following two questions: When is $R[x]/I$ Frobenius? When is $R[x]/I$ Frobenius and local? We develop algorithms for answering both questions. When the nilpotency of $\text{rad}
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Matrices over polynomial rings approached by commutative algebra

The main goal of the paper is the discussion of a deeper interaction between matrix theory over polynomial rings over a field and typical methods of commutative algebra and related algebraic geometry. This is intended in the sense of bringing numerical algebraic invariants into the picture of determinantal ideals, with an emphasis on non-generic ones ...
Ramos, Zaqueu, Simis, Aron
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Skew Constacyclic Codes over a Non-Chain Ring. [PDF]

Entropy (Basel), 2023
Köroğlu ME, Sarı M.
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