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.
Characterization of a radical of group rings over finite prime fields.
Compatible ideals and radicals of Ore extensions.
Complete radicals of some group rings.
Completely Prime Radical and Primary Ideal Representations in Non-Commutative Rings.
Corrigendum to: “A concrete analysis of the radical concept".
Ein Radikal für Fastringe.
Essential Cover and Closure
2000 Mathematics Subject Classification: 16N80, 16S70, 16D25, 13G05.We construct some new examples showing that Heyman and Roos construction of the essential closure in the class of associative rings can terminate at any finite or the first infinite ordinal.
Hereditariness, strongness and relationship between Brown-McCoy and Behrens radicals.
Hereditary right Jacobson radical of type- for right near-rings.
Kurosh-Amitsur radical theory for groups.
Kurosh-Amitsur right Jacobson radical of type 0 for right near-rings.
Mal'tsev--Neumann products of semi-simple classes of rings
Malt’tsev–Neumann products of semi-simple classes of associative rings are studied and some conditions which ensure that such a product is again a semi-simple class are obtained. It is shown that both products, and of semi-simple classes and are semi-simple classes if and only if they are equal.
Medial rings and an associated radical