Geodesic
On the compressive radical of semigroups
Sbornik. Mathematics, Tome 21 (1973) no. 4, pp. 523-534 
E. N. Roiz. On the compressive radical of semigroups. Sbornik. Mathematics, Tome 21 (1973) no. 4, pp. 523-534. http://geodesic.mathdoc.fr/item/SM_1973_21_4_a2/
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     url = {http://geodesic.mathdoc.fr/item/SM_1973_21_4_a2/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A centered right $S$-polygon (synonyms: $S$-operand, $S$-system) $A$ is called right compressive if $AS\ne0$ and $\alpha a=\alpha b\to\alpha=0\vee(a,b)\in(\operatorname{Ker}A)_S$ and leftt compressive if $AS\ne0$ and $\alpha a=\beta a\to\alpha=\beta\vee Aa=0$. Here $(\operatorname{Ker}A)_S$ is the congruence on the semigroup $S$ called the kernel of the $S$-polygon $A$ which is defined as follows: $(a,b)\in(\operatorname{Ker}A)_S\leftrightarrow(\forall\,\alpha\in A)(\alpha a=\alpha b)$. The intersection of the kernels of all right (left) compressive $S$-polygons is called the right (left) compressive radical of $S$. In this paper we study compressively semisimple and compressively radical semigroups. Bibliography: 11 titles.

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