Geodesic
Structure of Rings with Involution Applied to Generalized Polynomial Identities
Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 573-584

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Rowen, Louis Halle. Structure of Rings with Involution Applied to Generalized Polynomial Identities. Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 573-584. doi: 10.4153/CJM-1975-068-3
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[1] 1. Amitsur, S. A., Generalized polynomial identities and pivotal monomials, Trans. Amer. Math. Soc. 114 (1965), 210–226. Google Scholar

[2] 2. Amitsur, S. A., Prime rings having polynomial identities with arbitrary coefficients, Proc. London Math. Soc. 17 (1967), 470–486. Google Scholar

[3] 3. Amitsur, S. A., Identities in rings with involutions, Israel J. Math. 7 (1969), 63–68. Google Scholar

[4] 4. Amitsur, S. A., On rings of quotients, Instituto Nazionale di Alta Matematica, Symposia Matematica 8 (1972). Google Scholar

[5] 5. Baxter, W. E. and Martindale, W. S., III, Rings with involution and polynomial identities, Can. J. Math. 20 (1968), 465–473. Google Scholar

[6] 6. Herstein, I. N., Topics in ring theory (University of Chicago Press, Chicago, 1972). Google Scholar

[7] 7. Jacobson, N., Structure of rings, Amer. Math. Soc. Colloquium Publication XXXVII (1964). Google Scholar

[8] 8. Kochen, S., Ultraproducts in the theory of models, Ann. of Math. 74 (1961), 221–261. Google Scholar

[9] 9. Martindale, W. S., III, Rings with involution and polynomial identities, J. Algebra 11 (1969), 186–194. Google Scholar

[10] 10. Martindale, W. S., Prime rings satisfying a generalized polynomial identity, J. Algebra 12 (1969), 576–584. Google Scholar

[11] 11. Martindale, W. S., Prime rings with involution and generalized polynomial identities, J. Algebra 22 (1972), 502–516. Google Scholar

[12] 12. Rowen, L. H., On classical quotients of polynomial identity rings with involution, Proc. Amer. Math. Soc. 40 (1973), 23–29. Google Scholar

[13] 13. Rowen, L. H., Maximal quotients of semiprime Pi-algebras, Trans. Amer. Math. Soc. 196 (1974), 127–135. Google Scholar

[14] 14. Rowen, L. H., Generalized polynomial identities (to appear in J. Algebra, 1975). Google Scholar

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