17 citations · 56 across the 8 of their papers we have counts for
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math.RA2025
Algebraization of infinite summation
Pace P. Nielsen
An algebraic framework in which to study infinite sums is proposed, complementing and augmenting the usual topological tools. The framework subsumes numerous examples in the litera…
math.RA2015
Connections between unit-regularity, regularity, cleanness, and strong cleanness of elements and rings
Pace P. Nielsen, Janez Šter
We construct an example of a unit-regular ring which is not strongly clean, answering an open question of Nicholson. We also characterize clean matrices with a zero column, and thi…
math.RA2004★ 14 cited
Countable and Full Exchange Rings
Pace P. Nielsen
We show that a suitable ring with a ``nice'' topology, in which convergent limits of units are units, is an \aleph_0-exchange ring. We generalize the argument to show that a semi-r…