It is well known that a polynomial f(X) over a commutative ring R with identity is nilpotent if and only if each coefficient of f(X) is nilpotent; and that f(X) is a zero divisor in R[ X ] if and only ...
The Rocky Mountain Journal of Mathematics, Vol. 40, No. 5 (2010), pp. 1481-1503 (23 pages) Given a commutative semigroup S with 0, where 0 is the unique singleton ideal, we associate a simple graph ...
Three conjectures on group rings of torsion-free groups are commonly attributed to Kaplansky, namely the unit, zero divisor and idempotent conjectures. For example ...
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