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On Extensions of Chain Algebras and Atoms of the Lattice of Radicals |
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| Authors: | H. France-Jackson R. Mazurek E. R. Puczyłowski |
| Affiliation: | 1. Department of Mathematics and Applied Mathematics , Nelson Mandela Metropolitan University , Port Elizabeth, South Africa cbf@easterncape.co.uk;3. Faculty of Computer Science , Bia?ystok Technical University , Bia?ystok, Poland;4. Institute of Mathematics, University of Warsaw , Warsaw, Poland |
| Abstract: | In this article we study the problem when a left distributive algebra over a field determines an atom of the lattice of all radicals of rings. We show that this problem is strictly connected with the problem of describing extensions of left chain algebras and give a characterization of left chain algebras determining atoms. |
| Keywords: | Atom of the lattice of radicals Lattice of radicals Left chain algebra Left distributive algebra Lower radical |