Results 191 to 200 of about 46,367 (229)
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Jacobson - rings and hilbert algebras with polynomial identities
Annali di Matematica Pura ed Applicata, 1966We consider n-tuples of m × m matrices as zeroes of non-commutative polynomials in n-variables and establish an analogue of the classical Hilbert-Nullstellensatz. We study then finitely generated non-commutative algebras over Jacobson rings and obtain results conpletely analogous with the commutative tehory.
Amitsur, S. A., Procesi, C.
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B-rings with a polynomial identity
Journal of Soviet Mathematics, 1985Translation from Tr. Semin. Im. I. G. Petrovskogo 7, 232-238 (Russian) (1981; Zbl 0497.16008).
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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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Azumaya algebras and rings with polynomial identity
Mathematical Proceedings of the Cambridge Philosophical Society, 1976The Formanek polynomial gives an explicit expression for the calculation of central elements in a prime ring with polynomial identity, in such a form as to provide a set of linear maps of the ring into its centre. This note makes use of properties of these maps with the object of giving a direct proof of the remarkable theorem of M.
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Rings with a polynomial identity
2011Since Kaplansky's first paper on the subject of P.I. rings appeared in 1948, many fruitful results have arisen from the study of such rings. This thesis attempts to present the most important of these results in a unified theory. Chapter I gives the basic notation, definitions, a number of small lemmas together with Kaplansky's incisive result on ...
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Identities with generalized derivations on multilinear polynomials in prime rings
Afrika Matematika, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dhara, Basudeb +2 more
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Azumaya algebras and rings with polynomial identity (Addendum)
Mathematical Proceedings of the Cambridge Philosophical Society, 1976In the paper published in Mathematical Proceedings 79, 393–399, there is a gap in the proof of Theorem 2 which may present a difficulty to the reader. It occurs in the proof of non-degeneracy of the map g in the ring of matrices Zn, where Z is a finite field.
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Mediterranean Journal of Mathematics, 2013
For \(G\in\text{End}((R,+))\) and \(g\in\text{Der}(R)\) the pair \((G,g)\) is a generalized derivation of \(R\) if for all \(x,y\in R\), \(G(xy)=G(x)y+xg(y)\). Let \(R\) be a prime ring with \(\text{char\,}R\neq 2\) and extended centroid \(C\), and let \(f(X)\in C\{x_1,\ldots,x_n\}\) be a nonzero, multilinear, polynomial in noncommuting indeterminates ...
F. Rania, SCUDO, GIOVANNI
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For \(G\in\text{End}((R,+))\) and \(g\in\text{Der}(R)\) the pair \((G,g)\) is a generalized derivation of \(R\) if for all \(x,y\in R\), \(G(xy)=G(x)y+xg(y)\). Let \(R\) be a prime ring with \(\text{char\,}R\neq 2\) and extended centroid \(C\), and let \(f(X)\in C\{x_1,\ldots,x_n\}\) be a nonzero, multilinear, polynomial in noncommuting indeterminates ...
F. Rania, SCUDO, GIOVANNI
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Structure of Rings with Involution Applied to Generalized Polynomial Identities
Canadian Journal of Mathematics, 1975In [14, §4], some theorems were obtained about generalized polynomial identities in rings with involution, but the statements had to be weakened somewhat because a structure theory of rings with involution had not yet been developed sufficiently to permit proofs to utilize enough properties of rings with involution.
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Communications in Algebra, 2016
Let R be a prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, F a nonzero generalized derivation of R, I an ideal of R, and f(x1,…, xn) a multilinear polynomial over C which is not central valued on R. If 0 ≠ a ∈ R such that for all u, v ∈ f(I), where f(I) is the set of all evaluations of f(x1,…, xn) in I,
R. K. Sharma, B. Dhara, S. K. Tiwari
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Let R be a prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, F a nonzero generalized derivation of R, I an ideal of R, and f(x1,…, xn) a multilinear polynomial over C which is not central valued on R. If 0 ≠ a ∈ R such that for all u, v ∈ f(I), where f(I) is the set of all evaluations of f(x1,…, xn) in I,
R. K. Sharma, B. Dhara, S. K. Tiwari
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