Geodesic
Periodic semi-groups in the ring of residue classes
Čebyševskij sbornik, Tome 13 (2012) no. 2, pp. 124-130.

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In this work the structure periodic semi-groups $S(m;n)$ have been learnt which are given by definite coorelation $X^n=X$, $n>1$ in the ring $Z_m$ of residue classes the modulo $m$. The main result which determines the structure $S(m;n)$ is expressed by correlation: $S(m;n)=\cup_{i\in I(m)}G(i)$, $G(i_1)\cap G(i_2)=\varnothing$, $i_1,i_2\in I_m$, $i_1\neq i_2$, where $G(i)$ — maximal undergroup (in sence [6]) is generated by idempotent $i$ of the semi-lattice $I(m)\subset Z_m$. 
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V. E. Firstov. Periodic semi-groups in the ring of residue classes. Čebyševskij sbornik, Tome 13 (2012) no. 2, pp. 124-130. http://geodesic.mathdoc.fr/item/CHEB_2012_13_2_a15/

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