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On the Variety Determined by Symmetric Quadratic Algebras

✍ Scribed by Irvin Roy Hentzel; Luiz Antonio Peresi; Osmar Francisco Giuliani

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
92 KB
Volume
233
Category
Article
ISSN
0021-8693

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✦ Synopsis

We consider some polynomial identities of degree ≀ 5 which are satisfied by all symmetric quadratic algebras. We call rings satisfying these identities generalized quadratic rings, or GQ-rings. We show that when the ring is not flexible, these identities are enough to make the ring quadratic over its center. Therefore, simple nonflexible GQ-rings are symmetric quadratic algebras over their center, which is a field. For prime GQ-rings, the center has no nonzero zero divisors. Prime GQ-rings, which are not flexible, are subrings of the quadratic algebra formed by extending the center to its field of quotients. Flexible GQ-rings are noncommutative Jordan

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