Summary
A radical R, in the sense of Kurosh--Amitsur, is said to be compact if, given any collection of radicals X such that R ≤;VX, we have R ≤;VX' for some finite subcollection X' of X. A ring A is said to be radical compact if the lower radical on the singleton {A} is compact. This paper explores the relationship between radical compact rings and rings satisfying certain finiteness conditions. Closure properties of the class of all radical compact rings are also investigated.
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van den Berg, J. Compact elements in the lattice of radicals. Acta Math Hung 107, 177–186 (2005). https://doi.org/10.1007/s10474-005-0188-9
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DOI: https://doi.org/10.1007/s10474-005-0188-9