Results 31 to 40 of about 199,681 (176)

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, Johansson, Thomas, Löndahl, Carl   +2 more
core   +1 more source

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., Madill, Blake W., Shinko, Forte   +2 more
openaire   +3 more sources

Apolarity, Hessian and Macaulay polynomials [PDF]

, 2012
A result by Macaulay states that an Artinian graded Gorenstein ring R of socle dimension one and socle degree b can be realized as the apolar ring of a homogeneous polynomial f of degree b.
Alexander J., Ciliberto C., Dolgachev I., Eisenbud D., Elisa Postinghel, Geramita A. V., Iarrobino A., Iliev A., Iliev A., Lorenzo Di Biagio, Macaulay F. S., Ranestad K., Reichstein B.   +12 more
core   +2 more sources

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
doaj   +1 more source

On Nil-Symmetric Rings

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
doaj   +1 more source

Some Extensions of Generalized Morphic Rings and EM-rings

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018
Let R be a commutative ring with unity. The main objective of this article is to study the relationships between PP-rings, generalized morphic rings and EM-rings. Although PP-rings are included in the later rings, the converse is not in general true.
Ghanem Manal, Abu Osba Emad
doaj   +1 more source

Polynomial rings of the chiral $SU(N)_{2}$ models

, 1998
Via explicit diagonalization of the chiral $SU(N)_{2}$ fusion matrices, we discuss the possibility of representing the fusion ring of the chiral SU(N) models, at level K=2, by a polynomial ring in a single variable when $N$ is odd and by a polynomial ...
A Lima-Santos, Caselle M, Di Francesco P, Dijkgraaf R, Fredenhagen K, Fuchs J, Gannon T, Gepner D, Kastler D, Rehren K-H, Vafa C, Zamolodchikov A B   +11 more
core   +1 more source

Non-linear Group Actions with Polynomial Invariant Rings and a Structure Theorem for Modular Galois Extensions

, 2010
Let $G$ be a finite $p$-group and $k$ a field of characteristic $p>0$. We show that $G$ has a \emph{non-linear} faithful action on a polynomial ring $U$ of dimension $n=\mathrm{log}_p(|G|)$ such that the invariant ring $U^G$ is also polynomial.
Fleischmann, Peter, Woodcock, Chris
core   +1 more source

Borel-type presentation of the torus-equivariant quantum K-ring of flag manifolds of type C

Forum of Mathematics, Sigma
We give a presentation of the torus-equivariant (small) quantum K-ring of flag manifolds of type C as an explicit quotient of a Laurent polynomial ring; our presentation can be thought of as a quantization of the classical Borel presentation of the ...
Takafumi Kouno, Satoshi Naito
doaj   +1 more source

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, Nadezhda S. Mogilevskaya   +1 more
doaj   +1 more source