Geodesic
Free $n$-nilpotent dimonoids
Algebra and discrete mathematics, Tome 16 (2013) no. 2, pp. 299-310.

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

We construct a free $n$-nilpotent dimonoid and describe its structure. We also characterize the least $n$-nilpotent congruence on a free dimonoid, construct a new class of dimonoids with zero and give examples of nilpotent dimonoids of nilpotency index $2$.
Keywords: $n$-nilpotent dimonoid, free $n$-nilpotent dimonoid, $0$-diband of subdimonoids, dimonoid, semigroup. 
@article{ADM_2013_16_2_a11,
     author = {A. V. Zhuchok},
     title = {Free $n$-nilpotent dimonoids},
     journal = {Algebra and discrete mathematics},
     pages = {299--310},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2013_16_2_a11/}
}
TY  - JOUR
AU  - A. V. Zhuchok
TI  - Free $n$-nilpotent dimonoids
JO  - Algebra and discrete mathematics
PY  - 2013
SP  - 299
EP  - 310
VL  - 16
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2013_16_2_a11/
LA  - en
ID  - ADM_2013_16_2_a11
ER  - 
%0 Journal Article
%A A. V. Zhuchok
%T Free $n$-nilpotent dimonoids
%J Algebra and discrete mathematics
%D 2013
%P 299-310
%V 16
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2013_16_2_a11/
%G en
%F ADM_2013_16_2_a11
A. V. Zhuchok. Free $n$-nilpotent dimonoids. Algebra and discrete mathematics, Tome 16 (2013) no. 2, pp. 299-310. http://geodesic.mathdoc.fr/item/ADM_2013_16_2_a11/

[1] J.-L. Loday, “Dialgebras”, Dialgebras and related operads, Lect. Notes Math., 1763, Springer-Verlag, Berlin, 2001, 7–66 | DOI | MR | Zbl

[2] M. Gould, K. A. Linton, A. W. Nelson, “Interassociates of monogenic semigroups”, Semigroup Forum, 68 (2004), 186–201 | DOI | MR | Zbl

[3] M. Gould, R. E. Richardson, “Translational hulls of polynomially related semigroups”, Czechoslovak Math. J., 33:1 (1983), 95–100 | MR | Zbl

[4] E. Hewitt, H. S. Zuckerman, “Ternary operations and semigroups”, Semigroups, Proc. Sympos. (Detroit, Michigan, 1968), 1969, 95–100 | MR

[5] B. Richter, Dialgebren, Doppelalgebren und ihre Homologie, Diplomarbeit, Universitat Bonn, 1997 http://www.math.uni-bonn.de/people/richter/ | Zbl

[6] N. A. Koreshkov, “$n$-tuple algebras of associative type”, Izv. Vyssh. Uchebn. Zaved. Mat., 12 (2008), 34–42 (in Russian) | MR | Zbl

[7] A. V. Zhuchok, “Commutative dimonoids”, Algebra and Discrete Math., 2 (2009), 116–127 | MR | Zbl

[8] A. I. Malcev, “Nilpotent semigroups”, Uchen. Zap. Ivanov. Gos. Ped. Inst., 4 (1953), 107–111 (in Russian) | MR

[9] B. H. Neumann, T. Taylor, “Subsemigroups of nilpotent groups”, Proc. Royal Soc. London, Ser. A, 274 (1963), 1–4 | DOI | MR | Zbl

[10] G. Lallement, “On nilpotency and residual finiteness in semigroups”, Pacific J. Math., 42:3 (1972), 693–700 | DOI | MR | Zbl

[11] E. Jespers, J. Okninski, “Nilpotent semigroups and semigroup algebras”, Journal of Algebra, 169 (1994), 984–1011 | DOI | MR | Zbl

[12] R. S. Kruse, D. T. Price, “On the classification of nilpotent rings”, Mathematische Zeitschrift, 113:3 (1970), 215–223 | DOI | MR | Zbl

[13] A. V. Zhuchok, “Free commutative dimonoids”, Algebra and Discrete Math., 9:1 (2010), 109–119 | MR

[14] A. V. Zhuchok, “Free rectangular dibands and free dimonoids”, Algebra and Discrete Math., 11:2 (2011), 92–111 | MR | Zbl

[15] A. V. Zhuchok, “Free normal dibands”, Algebra and Discrete Math., 12:2 (2011), 112–127 | MR | Zbl

[16] A. V. Zhuchok, “Free $(\ell r, rr)$-dibands”, Algebra and Discrete Math., 15:2 (2013), 295–304 | MR

[17] A. V. Zhuchok, “Dimonoids”, Algebra and Logic, 50:4 (2011), 323–340 | DOI | MR | Zbl

[18] A. H. Clifford, G. B. Preston, The algebraic theory of semigroups, v. 1, American Mathematical Society, 1964; v. 2, 1967

[19] A. V. Zhuchok, “Free dimonoids”, Ukr. Math. J., 63:2 (2011), 196–208 | DOI | MR | Zbl

[20] L. N. Shevrin, “Semigroups”: V. Artamonov, V. Salii, L. Skornyakov and others, General algebra, Sect. IV, v. 2, 1991, 11–191