منابع مشابه
Group Algebras and Enveloping Algebras with Nonmatrix and Semigroup Identities
Let K be a field of characteristic p > 0. Denote by ω(R) the augmentation ideal of either a group algebra R = K[G] or a restricted enveloping algebra R = u(L) over K. We first characterize those R for which ω(R) satisfies a polynomial identity not satisfied by the algebra of all 2× 2 matrices over K. Then, we examine those R for which ω(R) satisfies a semigroup identity (that is, a polynomial i...
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We describe those group algebras over fields of characteristic different from 2 whose units symmetric with respect to the classical involution, satisfy some group identity.
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The structure theory for Pi-algebras is well developed. Some results of this theory are classic now. One of them is Kaplansky's theorem which asserts that a primitive Pi-algebra is finite dimensional over its centre. Another example is the theorem of Nagata-Higman which asserts that any algebra over a field of zero characteristic satisfying identity x" = 0 is nilpotent. In 1957 A.I. Shirshov pr...
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Let $mathscr{L}$ be a commutative subspace lattice generated by finite many commuting independent nests on a complex separable Hilbert space $mathbf{H}$ with ${rm dim}hspace{2pt}mathbf{H}geq 3$, ${rm Alg}mathscr{L}$ the CSL algebra associated with $mathscr{L}$ and $mathscr{M}$ be an algebra containing ${rm Alg}mathscr{L}$. This article is aimed at describing the form of additive mapppi...
متن کاملGroup identities on the units of algebraic algebras with applications to restricted enveloping algebras
An algebra A is called a GI-algebra if its group of units A satisfies a group identity. We provide positive support for the following two open problems. 1. Does every algebraic GI-algebra satisfy a polynomial identity? 2. Is every algebraically generated GI-algebra locally finite? 2000Mathematics Subject Classification. 16R40; 16R50; 16U60; 17B35.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1971
ISSN: 0002-9939
DOI: 10.2307/2038154