Results 141 to 150 of about 88,077 (185)
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Israel Journal of Mathematics, 1974
This article contains two surveys: (A) A historical survey of the early literature of 1920–1950 in Polynomial Identities which follows the roots and sources of PI-rings. (B) A survey of the methods of constructing identities for matrix rings, since the identity of Wagner until the central identities of Formanek and Razmyslov and the rational identity ...
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This article contains two surveys: (A) A historical survey of the early literature of 1920–1950 in Polynomial Identities which follows the roots and sources of PI-rings. (B) A survey of the methods of constructing identities for matrix rings, since the identity of Wagner until the central identities of Formanek and Razmyslov and the rational identity ...
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Proceedings of the American Mathematical Society, 1985
This q-polynomial identity involves the number of inversions between multisets \((a_ 1,...,a_ n)\) and \((m-a_ 1,...,m-a_ n)\), and generalizes the recurrence identity for q-binomial (Gaussian) coefficients [\textit{I. P. Goulden} and \textit{D. M. Jackson}, Combinatorial enumeration (1983; Zbl 0519.05001), p.
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This q-polynomial identity involves the number of inversions between multisets \((a_ 1,...,a_ n)\) and \((m-a_ 1,...,m-a_ n)\), and generalizes the recurrence identity for q-binomial (Gaussian) coefficients [\textit{I. P. Goulden} and \textit{D. M. Jackson}, Combinatorial enumeration (1983; Zbl 0519.05001), p.
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Poisson polynomial identities II
Archiv der Mathematik, 1999The commutative algebra \(B\) equipped with a bracket \(\{\cdot,\cdot\}\) is called a Poisson algebra if the bracket makes \(B\) a Lie algebra and is assumed to be an associative algebra derivation in each argument. In a series of papers, the author has attempted to develop a purely algebraic theory of Poisson algebras.
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Homogeneous polynomial identities
Israel Journal of Mathematics, 1982PI-algebras are studied by attaching invariants to the homogeneous identities analogous to the invariants of the multilinear identities studied by Regev. Also, it is shown that every finitely generated PI-algebra is polynomially bounded.
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Communications in Algebra, 1998
We study Poisson polynomial identities for the symmetric Poisson algebra of a Lie algebra and for the graded Poisson algebra associated to a ring of differential operators. Connections are made among degrees of identities, coadjoint orbits and Krull dimension.
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We study Poisson polynomial identities for the symmetric Poisson algebra of a Lie algebra and for the graded Poisson algebra associated to a ring of differential operators. Connections are made among degrees of identities, coadjoint orbits and Krull dimension.
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Communications in Algebra, 2002
ABSTRACT We describe an efficient way to use the Sn -module structure in the computation of the multilinear identities of degree n of a given algebra. The method was used to show that (where G is the Grassmann algebra) has identities of degree 8, but of no smaller degree. Explicit identities of degree 8 are given.
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ABSTRACT We describe an efficient way to use the Sn -module structure in the computation of the multilinear identities of degree n of a given algebra. The method was used to show that (where G is the Grassmann algebra) has identities of degree 8, but of no smaller degree. Explicit identities of degree 8 are given.
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2002
Definitions. A ring R is a polynomial identity ring (or PI ring for short) if R satisfies a monic polynomial f ∈ ℤ 〈X〉. Here, ℤ〈X〉 is the free ℤ-algebra on a finite set, X={x 1,...,x m } and to say that R satisfies f=f(x 1,...,x m ) means f(r 1,...,r m )=0 for all r 1,...,r m ∈ R.
Ken A. Brown, Ken R. Goodearl
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Definitions. A ring R is a polynomial identity ring (or PI ring for short) if R satisfies a monic polynomial f ∈ ℤ 〈X〉. Here, ℤ〈X〉 is the free ℤ-algebra on a finite set, X={x 1,...,x m } and to say that R satisfies f=f(x 1,...,x m ) means f(r 1,...,r m )=0 for all r 1,...,r m ∈ R.
Ken A. Brown, Ken R. Goodearl
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Israel Journal of Mathematics, 2022
Tensor polynomial identities generalize the concept of polynomial identities on d × d matrices to identities on tensor product spaces. Here we completely characterize a certain class of tensor polynomial identities in terms of their associated Young diagrams.
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Tensor polynomial identities generalize the concept of polynomial identities on d × d matrices to identities on tensor product spaces. Here we completely characterize a certain class of tensor polynomial identities in terms of their associated Young diagrams.
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An Identity in Hermite Polynomials
Biometrika, 1971SUMMARY An extension of the Runge (1914) identity in Hermite polynomials is derived, and a test of the assumption of bivariate normality is developed using the identity.
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Identity polynomials and test polynomials
2010The author investigates the relations between an identity polynomial \(p\in k[x_1, \dots, x_n]\), \(k\) a commutative field, and its zero set with respect to be an identity or determining set. In an analogous way he relates test polynomials and test sets. Furthermore conditions for being or not being an identity or test polynomial are derived.
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