Periodic semigroups in the ring of residue classes (Q2857921)
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scientific article; zbMATH DE number 6229101
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Periodic semigroups in the ring of residue classes |
scientific article; zbMATH DE number 6229101 |
Statements
19 November 2013
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idempotent modulo \(m\)
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subgroup of the multiplicative semigroup modulo \(m\)
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Periodic semigroups in the ring of residue classes (English)
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It follows from the theory of periodic semigroups \(S\) that to every idempotent \(i\) of \(S\) there corresponds a (unique) maximal subgroup \(S(i)\) of \(S\). The main result of the paper says that the semigroup of solutions of the congruence \(x^n\equiv x\pmod m\) in the ring \(\mathbb Z_m\) of residue classes modulo \(m\) can be written as the union of these maximal subgroups of \(\mathbb Z_m\).
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