A concrete analysis of the radical concept.
A generalization of the prime radical of an ideal.
A non-semiprime associative algebra with zero weak radical.
The weak radical, W-Rad(A) of a non-associative algebra A, has been introduced by A. Rodríguez Palacios in [3] in order to generalize the Johnson's uniqueness of norm theorem to general complete normed non-associative algebras (see also [2] for another application of this notion). In [4], he showed that if A is a semiprime non-associative algebra with DCC on ideals, then W-Rad(A) = 0. In the first part of this paper we give an example of a non-semiprime associative algebra A with DCC on ideals and...
A Note on Radicals and Polynomial Rings.
A radical for right near-rings: the right Jacobson radical of type-0.
Adjoint regular rings.
Are zero-symmetric simple nearrings with identity equiprime?
We show that there exist zero-symmetric simple nearrings with identity, which are not equiprime, solving a longstanding open problem.