Geodesic
Free $(\ell r, rr)$-dibands
Algebra and discrete mathematics, Tome 15 (2013) no. 2, pp. 295-304

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We prove that varieties of $(\ell r, rr)$-dibands and $(\ell n, rn)$-dibands coincide and describe the structure of free $(\ell r, rr)$-dibands. We also show that operations of an idempotent dimonoid with left (right) regular bands coincide, construct a new class of dimonoids and for such dimonoids give an example of a semiretraction.
Keywords: left (right) regular band, rr)$-diband, diband of subdimonoids, dimonoid, semigroup.
Mots-clés : $(\ell r 
@article{ADM_2013_15_2_a11,
     author = {A. V. Zhuchok},
     title = {Free $(\ell r, rr)$-dibands},
     journal = {Algebra and discrete mathematics},
     pages = {295--304},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2013_15_2_a11/}
}
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A. V. Zhuchok. Free $(\ell r, rr)$-dibands. Algebra and discrete mathematics, Tome 15 (2013) no. 2, pp. 295-304. http://geodesic.mathdoc.fr/item/ADM_2013_15_2_a11/