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Structure of Rings with Involution Applied to Generalized Polynomial Identities

  • Louis Halle Rowen (a1)

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In [14, §4], some theorems were obtained about generalized polynomial identities in rings with involution, but the statements had to be weakened somewhat because a structure theory of rings with involution had not yet been developed sufficiently to permit proofs to utilize enough properties of rings with involution. In this paper, such a theory is developed. The key concept is that of the central closure of a ring with involution, given in § 1, shown to have properties analogous to the central closure of a ring without involution. In § 2, the theory of primitive rings with involution, first set forth by Baxter-Martindale [5], is pushed forward, to enable a setting of generalized identities in rings with involution which can parallel the non-involutory situation.

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References

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1. Amitsur, S. A., Generalized polynomial identities and pivotal monomials, Trans. Amer. Math. Soc. 114 (1965), 210226.
2. Amitsur, S. A., Prime rings having polynomial identities with arbitrary coefficients, Proc. London Math. Soc. 17 (1967), 470486.
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14. Rowen, L. H., Generalized polynomial identities (to appear in J. Algebra, 1975).
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Structure of Rings with Involution Applied to Generalized Polynomial Identities

  • Louis Halle Rowen (a1)

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