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  • Author or Editor: H. France-Jackson x
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Abstract  

A non-simple idempotent *-ring with zero centre is constructed and a negative answer to a question of G. Tzintzis concerning a hypoidempotent radical property is given.

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Abstract  

A radical α in the universal class of associative rings is called matric-extensible if α (R n) = (α (R))n for any ring R, and natural number n, where R n denotes the nxn matrix ring with entries from R. We investigate matric-extensibility of the lower radical determined by a simple ring S. This enables us to find necessary and sufficient conditions for the lower radical determined by S to be an atom in the lattice of hereditary matric-extensible radicals. We also show that this lattice has atoms which are not of this form. We then describe all atoms of the lattice, and show that it is atomic.

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Acta Mathematica Hungarica
Authors: H. France-Jackson and W. Leavitt

Abstract  

Special classes which generate the prime radical are investigated.

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Summary  

We continue our study of the lattice of matric-extensible radicals of associative rings. We  find some atoms generated by simple rings of the lattices of all matric-extensible radicals, matric-extensible supernilpotent radicals and matric-extensible special radicals. We consider *-rings, which were previously defined by the second author, and consider when they generate atoms of these lattices.

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