Journal ArticleDOI
Homogeneous polynomial identities
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In this article, it was shown that every finitely generated PI-algebra is polynomially bounded, where the invariants to the homogeneous identities are analogous to those of the multilinear identities studied by Regev.Abstract:
PI-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.read more
Citations
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Invariants and the ring of generic matrices
Edward Formanek,Edward Formanek +1 more
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Codimensions of T-ideals and Hilbert series of relatively free algebras
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Applications of hook Young diagrams to P.I. Algebras
A Berele,Amitai Regev +1 more
TL;DR: In this paper, the multiplicities mλ in the cocharacter χn(A) of (any P.I. algebra A) are polynomially bounded, and a hook containing χ n(A ⊗ B) is obtained from the hooks containing mλ.
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Cocharacter Sequences for Algebras with Hopf Algebra Actions
References
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Book
The Algebraic Structure of Group Rings
TL;DR: For a group G over an integral domain R the group ring R(G) is a free unitary i-module over the elements of G as a basis and in which the multiplication on G is extended linearly to yield an associative multiplication on R (G), becoming a ring with an identity.
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The Degree of Polynomial Growth of Finitely Generated Nilpotent Groups
TL;DR: Theorem 4.3 as mentioned in this paper shows that if a group G is polycyclic, it must be virtually nilpotent, which is a direct algebraic proof of Wolf's result.
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The Poincaré series of the ring of 2 × 2 generic matrices
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Algebras satisfying a capelli identity
TL;DR: In this article, it was shown that an algebra satisfies a Capelli identity if, and only if, all the Young diagrams associated with its cocharacters are of a bounded height.