Geodesic
Ideally $\mathcal{J}$-decomposable semigroups
Matematičeskie zametki, Tome 8 (1970) no. 6, pp. 681-691.

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We consider ideally $\mathcal{J}$-decomposable semigroups ($\mathcal{J}$ –— is a system of semigroup identities). It is proved that every ideally $\mathcal{J}$-decomposable semigroup has a $\mathcal{J}$-decomposable series of ideals. 
@article{MZM_1970_8_6_a0,
     author = {L. M. Martynov},
     title = {Ideally $\mathcal{J}$-decomposable semigroups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {681--691},
     publisher = {mathdoc},
     volume = {8},
     number = {6},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_6_a0/}
}
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L. M. Martynov. Ideally $\mathcal{J}$-decomposable semigroups. Matematičeskie zametki, Tome 8 (1970) no. 6, pp. 681-691. http://geodesic.mathdoc.fr/item/MZM_1970_8_6_a0/