Geodesic
One-sided principal ideals in the direct product of two semigroups
Mathematica Bohemica, Tome 118 (1993) no. 4, pp. 337-342.

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A necessary and sufficient condition is given for a) a principal left ideal $L(s,t)$ in $S\times T$ to be equal to the direct product of the corresponding principal left ideals $L(s)\times L(t)$, b) an $\Cal L$-class $L_{(s,t)}$ to be equal to the direct product of the corresponding $\Cal L$-classes $L_s\times L_t$.
DOI : 10.21136/MB.1993.126156
Classification : 20M10, 20M12, 20M15
Keywords: principal left ideal; direct product; direct product of two semigroups 
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Fabrici, Imrich. One-sided principal ideals in the direct product of two semigroups. Mathematica Bohemica, Tome 118 (1993) no. 4, pp. 337-342. doi : 10.21136/MB.1993.126156. http://geodesic.mathdoc.fr/articles/10.21136/MB.1993.126156/

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