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Peter Danchev
Department of Mathematics, Plovdiv State University
Mathematics

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ON DECOMPOSITIONS OF NORMED UNITS IN ABELIAN GROUP RINGS Danchev, Peter
Journal of the Indonesian Mathematical Society Volume 18 Number 1 (April 2012)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.18.1.106.21-29

Abstract

We strengthen some results of W. L. May (J. Algebra, 1976) by findinga criterion when a special decomposition of normed units in abelian group ringsholds.DOI : http://dx.doi.org/10.22342/jims.18.1.106.21-29
WHEN IS AN ABELIAN WEAKLY CLEAN RING CLEAN? Danchev, Peter
Journal of the Indonesian Mathematical Society Volume 21 Number 2 (October 2015)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.21.2.229.83-91

Abstract

We answer the title question in the armative by showing that anyabelian weakly clean ring for which 2 belongs to its Jacobson radical (in particular, if 2 is nilpotent) has to be clean. Some constructive examples, one of which illustrates that this is no longer true removing the condition on the 2, are given as well.DOI : http://dx.doi.org/10.22342/jims.21.2.229.83-91
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