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.
متن کاملA new proof of the Frobenius conjecture on the dimensions of real algebras without zero divisors
A new way to prove the Frobenius conjecture on the dimensions of real algebras without zero divisors is given in the present paper. Firstly, the proof of nonexistence of real algebras without zero divisors in all dimensions except 1,2,4 and 8 was given in [1]. It was based on the simplicial cohomology operation technique. Later on the methods of K-theory cohomology operations gave one a possibi...
متن کاملSYMMETRIC m-CONVEX ALGEBRAS WITHOUT ALGEBRAIC ZERO DIVISORS AND RESULTS OF GELFAND-MAZUR TYPE
We show that in a symmetric m-convex algebra without algebraic zero divisors, any self-adjoint and invertible element is either positive or negative. As a consequence we obtain that a symmetric m-convex algebra containing no algebraic zero divisors and for which every positive element has a positive square root is isomorphic to C + Rad(A).
متن کاملm-CONVEX ALGEBRAS WITHOUT ALGEBRAIC ZERO DIVISORS AND RESULTS OF GELFAND-MAZUR TYPE
We show that in a symmetric m-convex algebra without algebraic zero divisors, any self-adjoint and invertible element is either positive or negative. As a consequence we obtain that a symmetric m-convex algebra containing no algebraic zero divisors and for which every positive element has a positive square root is isomorphic to C + Rad(A).
متن کاملConstructing zero divisors in the higher dimensional Cayley-Dickson algebras
In this paper we give methods to construct zero divisors in the Cayley–Dickson algebras An=R 2 for n larger than 4. Also we relate the set of zero divisors with suitable Stiefel manifolds.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1976
ISSN: 0021-8693
DOI: 10.1016/0021-8693(76)90255-6