A polynomial ring that is Jacobson radical and not nil
Copyright policy )A polynomial ring that is Jacobson radical and not nil
\textit{S. A. Amitsur} [Can. J. Math. 8, 355-361 (1956; Zbl 0072.02404)] conjectured that if a polynomial ring in one indeterminate is Jacobson radical, then it is a nil ring. The authors show that this conjecture does not hold. They construct an algebra over a countable field, the polynomial algebra in one indeterminate over which is Jacobson radical but not a nil ring.
- Polish Academy of Sciences Poland
- Polish Academy of Learning Poland
- Institute of Mathematics Poland
- University of Warsaw Poland
nil rings, Nil and nilpotent radicals, sets, ideals, associative rings, Jacobson radical rings, Ordinary and skew polynomial rings and semigroup rings, polynomial rings, Jacobson radical, quasimultiplication
nil rings, Nil and nilpotent radicals, sets, ideals, associative rings, Jacobson radical rings, Ordinary and skew polynomial rings and semigroup rings, polynomial rings, Jacobson radical, quasimultiplication
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