Space of minimal prime ideals of a ring without nilpotent elements |
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Authors: | NK Thakare SK Nimbhorkar |
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Institution: | Department of Mathematics, Technical University of Prague, 166 27 Prague 6, Czechoslovakia;Department of Mathematics, Prague Institute of Chemical Technology, 166 28 Prague 6, Czechoslovakia. |
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Abstract: | Hull-kernel topology on the set ∑(R) of prime ideals of a ring R with unity and without nilpotent elements is discussed. The restriction of this topology to the set π(R) of minimal prime ideals of R has been investigated in detail. The compactness of π(R) has been characterized in several ways. An interesting characterization of Baer rings is given.A functorial correspondence between the category of rings having the property that every prime ideal contains a unique minimal prime ideal and their minimal spectra is established. |
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