Finite submonoids of free left regular bands with unit
Algebra i logika, Tome 59 (2020) no. 6, pp. 680-701.

Voir la notice de l'article provenant de la source Math-Net.Ru

We deal with subsemigroups of a free left regular band ${\mathcal{F}}_n$ of rank $n$. It is proved that any finite, right hereditary, left regular band with a linearly ordered support semilattice is embedded in ${\mathcal{F}}_n$ for some $n$.
Keywords: free left regular band, submonoid, subsemigroup, support semilattice.
@article{AL_2020_59_6_a3,
     author = {A. N. Shevlyakov},
     title = {Finite submonoids of free left regular bands with unit},
     journal = {Algebra i logika},
     pages = {680--701},
     publisher = {mathdoc},
     volume = {59},
     number = {6},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2020_59_6_a3/}
}
TY  - JOUR
AU  - A. N. Shevlyakov
TI  - Finite submonoids of free left regular bands with unit
JO  - Algebra i logika
PY  - 2020
SP  - 680
EP  - 701
VL  - 59
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2020_59_6_a3/
LA  - ru
ID  - AL_2020_59_6_a3
ER  - 
%0 Journal Article
%A A. N. Shevlyakov
%T Finite submonoids of free left regular bands with unit
%J Algebra i logika
%D 2020
%P 680-701
%V 59
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2020_59_6_a3/
%G ru
%F AL_2020_59_6_a3
A. N. Shevlyakov. Finite submonoids of free left regular bands with unit. Algebra i logika, Tome 59 (2020) no. 6, pp. 680-701. http://geodesic.mathdoc.fr/item/AL_2020_59_6_a3/

[1] K. S. Brown, “Semigroups, rings and Markov chains”, J. Theor. Probab., 13:3 (2000), 871–938 | DOI | MR | Zbl

[2] S. Margolis, F. Saliola, B. Steinberg, “Semigroups embeddable in hyperplane face monoids”, Semigroup Forum, 89:1 (2014), 236–248 | DOI | MR | Zbl

[3] S. Margolis, F. Saliola, B. Steinberg, “Combinatorial topology and the global dimension of algebras arising in combinatorics”, J. Eur. Math. Soc. (JEMS), 17:12 (2015), 3037–3080 | DOI | MR | Zbl

[4] A. N. Shevlyakov, “O podpolugruppakh svobodnykh levoregulyarnykh polugrupp”, Vestnik Omskogo un-ta, 23:3 (2018), 56–58

[5] E. Daniyarova, A. Myasnikov, V. Remeslennikov, “Unification theorems in algebraic geometry”, Aspects of infinite groups, A Festschrift in honor of A. Gaglione, Papers of the conf. (Fairfield, USA, March, 2007), Algebra Discr. Math. (Hackensack), 1, eds. B. Fine et al., World Sci., Hackensack, NJ, 2008, 80—111 | MR | Zbl

[6] E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraicheskaya geometriya nad algebraicheskimi sistemami. II. Osnovaniya”, Fundam. i prikl. matem., 17:1 (2011/2012), 65–106 | MR

[7] O. G. Kharlampovich, A. G. Myasnikov, V. N. Remeslennikov, D. E. Serbin, “Subgroups of fully residually free groups: algorithmic problems”, Group theory, statistics, and cryptography, AMS special session combinatorial and statistical group theory (New York Univ., NY, USA, April 12–13, 2003), Contemp. Math., 360, eds. A. G. Myasnikov et al., Am. Math. Soc., Providence, RI, 2004, 63–101 | DOI | MR | Zbl

[8] I. Bumagin, O. Kharlampovich, A. Miasnikov, “The isomorphism problem for finitely generated fully residually free groups”, J. Pure Appl. Algebra, 208:3 (2007), 961–977 | DOI | MR | Zbl