Absolute zero divisors and local nilpotence in alternative algebras
نویسندگان
چکیده
منابع مشابه
On the Zero Divisors of Hopf Algebras
In an attempt to study the zero divisors in infinite Hopf algebras, we study two non-trivial examples of non-group ring infinite Hopf algebras and show that a variant of Kaplansky’s classical zero divisor conjecture holds for these two Hopf algebras.
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In an algebra class, one uses the zero-factor property to solve polynomial equations. For example, consider the equation x 2 = x. Rewriting it as x (x − 1) = 0, we conclude that the solutions are x = 0, 1. However, the same equation in a different number system need not yield the same solutions. For example, in Z 6 (the integers modulo 6), not only 0 and 1, but also 3 and 4 are solutions. (Chec...
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In an attempt to study the zero divisors in Hopf algebras, we study four non-trivial examples of nongroup ring infinite Hopf algebras and show that a variant of Kaplansky’s classical zero divisor conjecture holds for these four Hopf algebras. In particular we proof that the Hopf algebra CG has no non-trivial zero-divisors for any infinite finitely generated group G. We then consider the zero di...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1975
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1975-0354795-1