Condensed Rings with Zero-Divisors # |
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Authors: | D D Anderson Tiberiu Dumitrescu |
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Institution: | 1. Department of Mathematics , The University of Iowa , Iowa City, Iowa, USA ddanders@math.uiowa.edu;3. Facultatea de Matematic? , Universitatea Bucures?ti , Bucharest, Romania |
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Abstract: | A commutative ring R with identity is condensed (respectively strongly condensed) if for each pair of ideals I, J of R, IJ = {ij | i ∈ I, j ∈ J} (resp., IJ = iJ for some i ∈ I or IJ = Ij for some j ∈ J). In a similar fashion we can define regularly condensed and regularly strongly condensed rings by restricting I and J to be regular ideals. We show that an arbitrary product of rings is condensed if and only if each factor is so, and that RX] is condensed if and only if R is von Neumann regular. A number of results known in the domain case are extended to the ring case. Regularly strongly condensed and one-dimensional regularly condensed Noetherian rings are characterized. |
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Keywords: | Condensed ring Strongly condensed ring |
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