Results 1  10
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2,794
Solvable polynomial rings
, 1992
"... This work treats solvable polynomial rings, which can be characterized as commutative polynomial rings with a new noncommutative multiplication , such that the product of two polynomials is the sum of a commutative polynomial, smaller with respect to a fixed quasi order on the polynomials and a he ..."
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Cited by 25 (1 self)
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This work treats solvable polynomial rings, which can be characterized as commutative polynomial rings with a new noncommutative multiplication , such that the product of two polynomials is the sum of a commutative polynomial, smaller with respect to a fixed quasi order on the polynomials and a
RADICALS AND POLYNOMIAL RINGS
 J. AUSTRAL. MATH. SOC. 72 (2002), 23–31
, 2002
"... We prove that polynomial rings in one indeterminate over nil rings are antiregular radical and uniformly strongly prime radical. These give some approximations of Köthe’s problem. We also study the uniformly strongly prime and superprime radicals of polynomial rings in noncommuting indeterminates. ..."
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Cited by 1 (0 self)
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We prove that polynomial rings in one indeterminate over nil rings are antiregular radical and uniformly strongly prime radical. These give some approximations of Köthe’s problem. We also study the uniformly strongly prime and superprime radicals of polynomial rings in noncommuting indeterminates
COMPUTATIONS IN WEIGHTED POLYNOMIAL RINGS
"... In this note we survey some results which are useful to perform algebraic computations in a weighted polynomial ring. Introduction and notation In this survey paper we consider nonstandard graded polynomial rings and take into examination some results concerning weighted Hilbert functions, weighted ..."
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In this note we survey some results which are useful to perform algebraic computations in a weighted polynomial ring. Introduction and notation In this survey paper we consider nonstandard graded polynomial rings and take into examination some results concerning weighted Hilbert functions
RingLWE in polynomial rings
 In Public Key Cryptography
, 2012
"... Abstract. The RingLWE problem, introduced by Lyubashevsky, Peikert, and Regev (Eurocrypt 2010), has been steadily finding many uses in numerous cryptographic applications. Still, the RingLWE problem defined in [LPR10] involves the fractional ideal R ∨ , the dual of the ring R, which is the source ..."
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Cited by 6 (0 self)
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of many theoretical and implementation technicalities. Until now, getting rid of R ∨ , required some relatively complex transformation that substantially increase the magnitude of the error polynomial and the practical complexity to sample it. It is only for rings R = Z[X]/(X n + 1) where n a power of 2
ON THE DIFFERENTIAL SIMPLICITY OF POLYNOMIAL RINGS
"... Abstract. Commutative differentially simple rings have proved to be quite useful as a source of examples in noncommutative algebra. In this paper we use the theory of holomorphic foliations to construct new families of derivations with respect to which the polynomial ring over a field of characteri ..."
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Cited by 2 (1 self)
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Abstract. Commutative differentially simple rings have proved to be quite useful as a source of examples in noncommutative algebra. In this paper we use the theory of holomorphic foliations to construct new families of derivations with respect to which the polynomial ring over a field
Endomorphisms of polynomial rings . . .
, 2006
"... The Jacobian Conjecture is established: If f1,...,fn be elements in a polynomial ring k[X1,..., Xn] over a field k of characteristic zero such that det(∂fi/∂Xj) is a nonzero constant, then k[f1,..., fn] = k[X1,..., Xn]. ..."
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The Jacobian Conjecture is established: If f1,...,fn be elements in a polynomial ring k[X1,..., Xn] over a field k of characteristic zero such that det(∂fi/∂Xj) is a nonzero constant, then k[f1,..., fn] = k[X1,..., Xn].
Reduced Gröbner Bases in Polynomial Rings over a Polynomial Ring
 proceedings of the International Conference on Mathematical Aspects of Computer and Information Sciences (MACIS
, 2006
"... Abstract. We define reduced Gröbner bases in polynomial rings over a polynomial ring and introduce an algorithm for computing them. There exist some algorithms for computing Gröbner bases in polynomial rings over a polynomial ring. However, we cannot obtain the reduced Gröbner bases by these algorit ..."
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Cited by 1 (1 self)
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Abstract. We define reduced Gröbner bases in polynomial rings over a polynomial ring and introduce an algorithm for computing them. There exist some algorithms for computing Gröbner bases in polynomial rings over a polynomial ring. However, we cannot obtain the reduced Gröbner bases
BOUNDS AND DEFINABILITY IN POLYNOMIAL RINGS
, 2004
"... We study questions around the existence of bounds and the dependence on parameters for linearalgebraic problems in polynomial rings over rings of an arithmetic flavour. In particular, we show that the module of syzygies of polynomials f 1; … ; f n [ RX1; … ; XNŠ with coefficients in a Prüfer doma ..."
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Cited by 4 (1 self)
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We study questions around the existence of bounds and the dependence on parameters for linearalgebraic problems in polynomial rings over rings of an arithmetic flavour. In particular, we show that the module of syzygies of polynomials f 1; … ; f n [ RX1; … ; XNŠ with coefficients in a Prüfer
Coding with skew polynomial rings
 J. Symbolic Comput
"... In analogy to cyclic codes, we study linear codes over finite fields obtained from left ideals in a quotient ring of a (non commutative) skew polynomial ring. The paper shows how existence and properties of such codes are linked to arithmetic properties of skew polynomials. This class of codes is a ..."
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Cited by 11 (3 self)
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In analogy to cyclic codes, we study linear codes over finite fields obtained from left ideals in a quotient ring of a (non commutative) skew polynomial ring. The paper shows how existence and properties of such codes are linked to arithmetic properties of skew polynomials. This class of codes is a
GOTZMANN IDEALS OF THE POLYNOMIAL RING
, 2007
"... Let A = K[x1,..., xn] denote the polynomial ring in n variables over a field K. We will classify all the Gotzmann ideals of A with at most n generators. In addition, we will study Hilbert functions H for which all homogeneous ideals of A with the Hilbert function H have the same graded Betti numbe ..."
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Cited by 2 (0 self)
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Let A = K[x1,..., xn] denote the polynomial ring in n variables over a field K. We will classify all the Gotzmann ideals of A with at most n generators. In addition, we will study Hilbert functions H for which all homogeneous ideals of A with the Hilbert function H have the same graded Betti
Results 1  10
of
2,794