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Journal of AlgebraWe compute the graded polynomial identities of the infinite dimensional upper triangular matrix algebra over an arbitrary field. If the grading group is finite, we prove that the set of graded polynomial identities admits a finite basis.
Felipe Yukihide Yasumura
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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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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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A New Approach to Polynomial Identities
The Ramanujan Journal, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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An identity for multivariate Bernstein polynomials
Computer Aided Geometric Design, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kurt Jetter, Joachim Stöckler
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Interprocedurally Analyzing Polynomial Identities
2006Since programming languages are Turing complete, it is impossible to decide for all programs whether a given non-trivial semantic property is valid or not. The way-out chosen by abstract interpretation is to provide approximate methods which may fail to certify a program property on some programs.
Markus Müller-Olm +2 more
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A Note on Generalized Polynomial Identities
Canadian Mathematical Bulletin, 1972Let A be an algebra with 1 over a field F and let B be a fixed F-basis of A. Let F〈x〉=F〈x1,…, xn,…,〉 be the free algebra over F in noncommutative indeterminates x1,…, xn,…, and denote by AF〈x〉 the free product of A and F〈x〉 over F. The elements of AF〈x〉 of the form varies, repetitions allowed) form an F-basis of AF〈x〉.
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On polynomial identities in nil-algebras
Journal of Mathematical Sciences, 2007The paper under review surveys several new results concerning non-finitely based T-ideals, that is ideals of identities in the free associative algebra which do not admit any finite generating set. According to Kemer's celebrated theory every T-ideal in characteristic 0 is finitely based. On the other hand, \textit{A. Ya. Belov} [Fundam. Prikl. Mat. 5,
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Identity polynomials and test polynomials
1997The 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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