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Polynomial Identities in Smash Products
Journal of Lie Theory, 2002For a Lie algebra \(L\), \(U(L)\) (respectively \(u(L)\)) denotes the (restricted) universal enveloping algebra of \(L\). The main results of the article are the following two theorems. Theorem 2.3. Let \(G\) be a group, \(L\) be a Lie algebra over a field \(K\) of characteristic \(p>0\) and \(G\) act on \(L\) by automorphisms. Then the smash product \(
Bahturin, Yuri, Petrogradsky, Victor
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Rings with Involution and Polynomial Identities
Canadian Journal of Mathematics, 1968An involution * of a ring A is a one-one additive mapping of A onto itself such that (xy)* = y*x* and x** = x for all x, y ∊ A. If A is an algebra over a field Φ, one makes the additional requirement that (λx)* = λx* for all λ ∊ Φ, x ∊ A. S will generally denote the set of symmetric elements s* = s, K the set of skew elements , and Z the centre of A.
Baxter, W. E., Martindale, W. S. III
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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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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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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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The Proof Complexity of Polynomial Identities
2009 24th Annual IEEE Conference on Computational Complexity, 2009Devising an efficient deterministic -- or even a non-deterministic sub-exponential time -- algorithm for testing polynomial identities is a fundamental problem in algebraic complexity and complexity at large. Motivated by this problem, as well as by results from proof complexity, we investigate the complexity of _proving_ polynomial identities. To this
Pavel Hrubes, Iddo Tzameret
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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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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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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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