A Characterization of the Jacobson Radical in Ternary Algebras

Hyo Chul Myung
1973 Proceedings of the American Mathematical Society  
The Jacobson radical Rad T for a ternary algebra T is characterized as one of the following: (i) the set of properly quasi-invertible elements in T; (ii) the set of xe T such that the principal right ideal (xTT) or left ideal (TTx) is quasi-regular in T; (iii) the unique maximal quasi-regular ideal in T; (iv) the set of xeT such that Rad Ttx) = T. We also obtain ternary algebraanalogs of characterization of the radicals of certain subalgebras in an associative algebra.
doi:10.2307/2039267 fatcat:liwxpxtezrfuppcveh3wecwsey