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Nonunits
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(Redirected from Nonunit)
Nonunits are elements of a set (e.g. of numbers, matrices, polynomials, ...) without a multiplicative inverse in the given set. Zero is a nonunit in any set (since 0 is the multiplicative absorption element, i.e. it cannot have a multiplicative inverse).
Nonunits in the set of integers
The nonunits in the set of integers are
- Zero
- Prime numbers (positive primes and their negative associates)
- Composite numbers (positive composites and their negative associates)
while the units are
- {–1, +1}
Nonunits in the set of matrices
Nonunit matrices have determinant equal to zero. (Matrices with nonzero determinant are invertible.)