caa a22 4500 388092157 CHVBK 20180307125254.0 cr unu---uuuuu 161130e199908 xx s 000 0 eng 10.1017/S0004972700033402 doi S0004972700033402 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700033402 On zero-dimensionality and fragmented rings [Elektronische Daten] A commutative ring R is said to be fragmented if each nonunit of R is divisible by all positive integral powers of some corresponding nonunit of R. It is shown that each fragmented ring which contains a nonunit non-zero-divisor has (Krull) dimension ∞. We consider the interplay between fragmented rings and both the atomic and the antimatter rings. After developing some results concerning idempotents and nilpotents in fragmented rings, along with some relevant examples, we use the "fragmented” and "locally fragmented” concepts to obtain new characterisations of zero-dimensional rings, von Neumann regular rings, finite products of fields, and fields. Copyright © Australian Mathematical Society 1999 Coykendall Jim Department of Mathematics North Dakota State University Fargo ND 58105-5075 United States of America Dobbs David E. Department of Mathematics University of Tennessee Knoxville TN 37996-1300 United States of America Mullins Bernadette Department of Mathematics and Statistics Youngstown State University Youngstown OH 44555-3302 United States of America Bulletin of the Australian Mathematical Society Cambridge University Press 60/1(1999-08), 137-151 0004-9727 60:1<137 1999 60 BAZ https://doi.org/10.1017/S0004972700033402 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700033402 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Coykendall Jim Department of Mathematics North Dakota State University Fargo ND 58105-5075 United States of America NATIONALLICENCE 700 1- Dobbs David E. Department of Mathematics University of Tennessee Knoxville TN 37996-1300 United States of America NATIONALLICENCE 700 1- Mullins Bernadette Department of Mathematics and Statistics Youngstown State University Youngstown OH 44555-3302 United States of America NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 60/1(1999-08), 137-151 0004-9727 60:1<137 1999 60 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge