Group rings, matrix rings, and polynomial identities
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- by Elizabeth Berman PDF
- Trans. Amer. Math. Soc. 172 (1972), 241-248 Request permission
Abstract:
This paper studies the question, if $R$ is a ring satisfying a polynomial identity, what polynomial identities are satisfied by group rings and matrix rings over $R$? Theorem 2.6. If $R$ is an algebra over a field with at least $q$ elements, and $R$ satisfies ${x^q} = 0$, and $G$ is a group with an abelian subgroup of index $k$, then the group ring $R(G)$ satisfies ${x^t} = 0$, where $t = q{k^2} + 2$. Theorem 3.2. If $R$ is a ring satisfying a standard identity, and $G$ is a finite group, then $R(G)$ satisfies a standard identity. Theorem 3.4. If $R$ is an algebra over a field, and $R$ satisfies a standard identity, then the $k$-by-$k$ matrix ring ${R_k}$ satisfies a standard identity. Each theorem specifies the degree of the polynomial identity.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 172 (1972), 241-248
- MSC: Primary 16A38
- DOI: https://doi.org/10.1090/S0002-9947-1972-0308184-8
- MathSciNet review: 0308184