Results 61 to 70 of about 199,681 (176)
Radicals Of Polynomial Rings [PDF]
Canadian Journal of Mathematics, 1956 Introduction. Let R be a ring and let R[x] be the ring of all polynomials in a commutative indeterminate x over R. Let J(R) denote the Jacobson radical (5) of the ring R and let L(R) be the lower radical (4) of R. The main object of the present note is to determine the radicals J(R[x]) and L(R[x]).
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NIL DERIVATIONS AND d-IDEALS ON POLYNOMIAL RINGS
BarekengLet be a ring. An additive mapping is called derivation if satisfies Leibniz's rule, i.e., for every In a special case, for each there exists a positive integer which depends on such that , then is called as a nil derivation on .
Ditha Lathifatul Mursyidah +3 more
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Canonical bases for subalgebras of factor algebras [PDF]
Computer Science Journal of Moldova, 1999 We introduce canonical bases for subalgebras of quotients of the commutative and non-commutative polynomial ring. The usual theory for Grobner bases and its counterpart for subalgebras of polynomial rings, also called SAGBI bases, are combined to obtain ...
P. Nordbeck
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Some strange behaviors of the power series ring R[[X]]
ITM Web of Conferences, 2018 Let R be a commutative ring with identity. Let R[X] and R[[X]] be the polynomial ring and the power series ring respectively over R. Being the completion of R[X] (under the X-adic topology), R[[X]] does not always share the same property with R[X].
Phan Thanh Toan
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Free field primaries in general dimensions: counting and construction with rings and modules
Journal of High Energy Physics, 2018 We define lowest weight polynomials (LWPs), motivated by so(d, 2) representation theory, as elements of the polynomial ring over d × n variables obeying a system of first and second order partial differential equations.
Robert de Mello Koch, Sanjaye Ramgoolam
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Simple ambiskew polynomial rings
Journal of Algebra, 2013 We determine simplicity criteria in characteristics 0 and $p$ for a ubiquitous class of iterated skew polynomial rings in two indeterminates over a base ring. One obstruction to simplicity is the possible existence of a canonical normal element $z$. In the case where this element exists we give simplicity criteria for the rings obtained by inverting $z$
Jordan, David A., Wells, Imogen E.
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The discrete logarithm problem in Bergman's non-representable ring
Journal of Mathematical Cryptology, 2012 Bergman's ring , parameterized by a prime number p, is a ring with p5 elements that cannot be embedded in a ring of matrices over any commutative ring. This ring was discovered in 1974.
Banin Matan, Tsaban Boaz
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Radical Structures of Fuzzy Polynomial Ideals in a Ring
Discrete Dynamics in Nature and Society, 2016 We investigate the radical structure of a fuzzy polynomial ideal induced by a fuzzy ideal of a ring and study its properties. Given a fuzzy ideal β of R and a homomorphism f:R→R′, we show that if fx is the induced homomorphism of f, that is, fx(∑i=0naixi)
Hee Sik Kim, Chang Bum Kim, Keum Sook So
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Radicals of skew polynomial rings and skew Laurent polynomial rings
Journal of Algebra, 2011 In this paper, \(R\) denotes an associative ring with identity, and \(\sigma\) stands for an automorphism of \(R\). \(W(R)\), \(L(R)\) and \(N(R)\) denote the Wedderburn radical, the Levitzki radical and the upper nil radical of \(R\), respectively. An ideal \(I\) of \(R\) is called a \(\sigma\)-ideal if \(\sigma(I)\subseteq I\).
Hong, Chan Yong +2 more
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria MatematicaLet S = ℤp[u, v]/〈u2, v2, uv − uv〉 be a semi-local ring, where p is a prime number. In the present article, we determine the generating sets of S and use them to construct the structures of ℤpS-additive cyclic and constacyclic codes.
Ashraf Mohammad +3 more
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