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A non-semiprime associative algebra with zero weak radical.

Abdelfattah Haily (1997)

Extracta Mathematicae

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...

Adjoint regular rings.

Heatherly, Henry E., Tucci, Ralph P. (2002)

International Journal of Mathematics and Mathematical Sciences

Essential Cover and Closure

Andruszkiewicz, R. (2004)

Serdica Mathematical Journal

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.

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