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On separable polynomials over a commutative ring
On separable polynomials over a commutative ringopenaire
On separable polynomials over a commutative ring IV
On separable polynomials over a commutative ring IVopenaire
On separable polynomials over a commutative rings III
On separable polynomials over a commutative rings IIIopenaire
On separable polynomials over a commutative ring II
On separable polynomials over a commutative ring IIopenaire
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On Polynomial Functions over Finite Commutative Rings
Acta Mathematica Sinica, English Series, 2006Not every function from a commutative ring \(R\) into itself is induced by a polynomial in \(R[x]\). For certain local rings the number of functions that arise from polynomials has been determined in [\textit{S. Frisch}, Polynomial functions on finite commutative rings. Advances in commutative ring theory.
Jiang, Jianjun +3 more
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Units of commutative group rings over polynomial ring
Asian-European Journal of Mathematics, 2018In this paper, we obtain the structure of the normalized unit group [Formula: see text] of the modular group algebra [Formula: see text], where [Formula: see text] is a finite abelian group and [Formula: see text] is the univariate polynomial ring over a finite field [Formula: see text] of characteristic [Formula: see text]
Kaur, S., Khan, M.
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Functions and polynomials over finite commutative rings
Aequationes Mathematicae, 2001Let \(R\) be a finite commutative ring. The authors derive an upper bound for the total number of functions from \(R\) to itself which can be represented by polynomials over \(R\). This extends earlier results for Galois rings of \textit{J. V. Brawley} and \textit{G. L. Mullen} [J. Number Theory 41, No. 2, 156--166 (1992; Zbl 0759.11043)].
Maxson CJ, Van Der Merwe AB
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On Authentication Schemes Using Polynomials Over Non Commutative Rings
Wireless Personal Communications, 2021Authentication is a term very important for data communication security. We see many frauds due to authentication failure. The problem manifolds when communication is over insecure channel. Entity authentication is a term which involves proof of sender’s identity and very useful in various applications like in banking sector and various other client ...
Varun Shukla +2 more
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A remark on polynomial function over finite commutative rings with identity
Boletim da Sociedade Brasileira de Matemática, 1979In the present paper, the degree of polynomial functions on a finite commutative ringR with identity is investigated. An upper bound for the degree is given (Theorem 3) with the help of a reduction formula for powers (Theorem 1).
Eigenthaler, Günther +1 more
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