Results 21 to 30 of about 199,462 (178)
Structure of a chain ring as a ring of matrices over a Galois ring
AIMS Mathematics, 2022 The structure of a finite chain ring has already been described by Wirt in 1972 and others later. The purpose of this article is to describe another structure of a finite chain ring as a ring of square matrices over Galois ring using the companion matrix
Yousef Alkhamees, Badr Alhajouj
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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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A New Algorithm for Solving Ring-LPN with a Reducible Polynomial [PDF]
, 2014 The LPN (Learning Parity with Noise) problem has recently proved to be of great importance in cryptology. A special and very useful case is the RING-LPN problem, which typically provides improved efficiency in the constructed cryptographic primitive.
Guo, Qian +2 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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Method of restoring multivariable Boolean function from its derivative
Advanced Engineering Research, 2017 Introduction. Boolean functions of several variables are of paramount importance in the coding theory and cryptography. The compositions of these functions are used in a set of the symmetric cryptosystems; therewith, some error-control codes, such as ...
Alexander V. Mazurenko +1 more
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Multiplicity of the saturated special fiber ring of height two perfect ideals [PDF]
, 2019 Let $R$ be a polynomial ring and $I \subset R$ be a perfect ideal of height two minimally generated by forms of the same degree. We provide a formula for the multiplicity of the saturated special fiber ring of $I$. Interestingly, this formula is equal to
Cid-Ruiz, Yairon
core +4 more sources
Strongly stable ideals and Hilbert polynomials [PDF]
, 2018 The \texttt{StronglyStableIdeals} package for \textit{Macaulay2} provides a method to compute all saturated strongly stable ideals in a given polynomial ring with a fixed Hilbert polynomial.
Alberelli, Davide, Lella, Paolo
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Reversible skew laurent polynomial rings and deformations of poisson automorphisms [PDF]
, 2009 A skew Laurent polynomial ring S = R[x(+/- 1); alpha] is reversible if it has a reversing automorphism, that is, an automorphism theta of period 2 that transposes x and x(-1) and restricts to an automorphism gamma of R with gamma = gamma(-1).
DAVID A. JORDAN +7 more
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When is R[x] a principal ideal ring?
Revista Integración, 2018 Because of its interesting applications in coding theory, cryptography, and algebraic combinatoris, in recent decades a lot of attention has been paid to the algebraic structure of the ring of polynomials R[x], where R is a finite commutative ring with ...
Henry Chimal-Dzul, C. A. López-Andrade
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Journal of Mathematics, 2014 The concept of nil-symmetric rings has been introduced as a generalization of symmetric rings and a particular case of nil-semicommutative rings. A ring R is called right (left) nil-symmetric if, for a,b,c∈R, where a,b are nilpotent elements, abc=0 (cab=
Uday Shankar Chakraborty, Krishnendu Das
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