Cover Image

Structure of relatively free trioids

Loday and Ronco introduced the notions of a~trioid and a trialgebra, and constructed the free trioid of rank \(1\) and the free trialgebra. This paper is a survey of recent developments in the study of free objects in the varieties of trioids and trialgebras. We present the constructions of the free...

Full description

Saved in:

Bibliographic Details
Date:	2021
Main Author:	Zhuchok, A. V.
Format:	Article
Language:	English
Published:	Lugansk National Taras Shevchenko University 2021
Subjects:	trioid trialgebra free trioid free trialgebra relatively free trioid semigroup 08B20 20M10 20M50 17A30 17D9
Online Access:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1732
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Algebra and Discrete Mathematics

Institution

Algebra and Discrete Mathematics

Similar Items

Certain verbal congruences on the free trioid
by: Zhuchok, Anatolii V.
Published: (2024)

Structure of relatively free \(n\)-tuple semigroups
by: Zhuchok, A. V.
Published: (2023)

Free rectangular dibands and free dimonoids
by: Zhuchok, Anatolii V.
Published: (2018)

Abelian doppelsemigroups
by: Zhuchok, Anatolii V., et al.
Published: (2019)

On one class of algebras
by: Zhuchok, Yuliia V.
Published: (2018)

Free abelian dimonoids
by: Zhuchok, Yurii
Published: (2016)

Automorphisms of the endomorphism semigroup of a free abelian diband
by: Zhuchok, Yurii V.
Published: (2018)

The free spectra of varieties generated by idempotent semigroups
by: Pluhar, Gabriella, et al.
Published: (2018)

Free \((\ell r, rr)\)-dibands
by: Zhuchok, Anatolii V.
Published: (2018)

Interassociativity and three-element doppelsemigroups
by: Gavrylkiv, Volodymyr, et al.
Published: (2020)

Note on cyclic doppelsemigroups
by: Gavrylkiv, V.
Published: (2023)

Automorphisms of the endomorphism semigroup of a free commutative \(g\)-dimonoid
by: Zhuchok, Yurii V.
Published: (2016)

Free products of semigroups defined by automata
by: Kochubinska, Eugenia, et al.
Published: (2025)

Construction of free \(\mathfrak{g}\)-dimonoids
by: Movsisyan, Yuri, et al.
Published: (2018)

Characterizing semigroups with commutative superextensions
by: Banakh, Taras, et al.
Published: (2018)

Sandwich semigroups and Brandt semigroups
by: Desiateryk, Oleksandra O., et al.
Published: (2024)

On the Cartesian product of the Menger algebras of terms and relational formulas
by: Kumduang, Thodsaporn
Published: (2025)

Free ultra-groups, generators and relations
by: Tolue, Behnaz, et al.
Published: (2020)

\(\mathcal{H-}\),\(\mathcal{R-}\)and \(\mathcal{L-}\)cross-sections of the infinite symmetric inverse semigroup \(IS_X\)
by: Pyekhtyeryev, Vasyl
Published: (2018)

\(\mathcal{H}\)- and \(\mathcal{R}\)-cross-sections of the full finite semigroup \(T_n\)
by: Pyekhtyeryev, Vasyl
Published: (2018)

Inner automorphisms of Lie algebras related with generic \(2\times 2\) matrices
by: Drensky, Vesselin, et al.
Published: (2018)

Free commutative dimonoids
by: Zhuchok, Anatolii V.
Published: (2018)

Idempotent \(\mathcal{D}\)-cross-sections of the finite inverse symmetric semigroup \(IS_n\)
by: Pyekhtyeryev, Vasyl
Published: (2018)

Length of the inverse symmetric semigroup
by: Ganyushkin, Olexandr, et al.
Published: (2018)

Finite automaton actions of free products of groups
by: Fedorova, Mariia, et al.
Published: (2017)

Endomorphisms of Clifford semigroups with injective structure homomorphisms
by: Worawiset, S., et al.
Published: (2021)

Representations and relative Rota-Baxter operators of Hom-Leibniz-Poisson algebras
by: Attan, Sylvain
Published: (2025)

\(\mathscr{L}\)-cross-sections of the finite symmetric semigroup
by: Bondar, Eugenja
Published: (2018)

Classification of \(\mathscr{L}\)-cross-sections of the finite symmetric semigroup up to isomorphism
by: Bondar, Eugenija
Published: (2016)

On a semitopological polycyclic monoid
by: Bardyla, Serhii, et al.
Published: (2016)

Characterization of finite simple semigroup digraphs
by: Meksawang, J., et al.
Published: (2018)

Representations of ordered doppelsemigroups by binary relations
by: Zhuchok, Yurii, et al.
Published: (2019)

On growth of the inverse semigroup of partially defined co–finite automorphisms of integers
by: Bezushchak, O.
Published: (2018)

On the semigroup of injective transformations with restricted range that equal gap and defect
by: Singha, Boorapa
Published: (2025)

On certain semigroups of contraction mappings of a finite chain
by: Umar, A., et al.
Published: (2022)

The Tits alternative for generalized triangle groups of type \((3,4,2)\)
by: Howie, James, et al.
Published: (2018)

On \(0\)-semisimplicity of linear hulls of generators for semigroups generated by idempotents
by: Bondarenko, Vitaliy M., et al.
Published: (2018)

Generators and relations for the semigroups of increasing functions on \(\mathbb{N}\) and \(\mathbb{Z}\)
by: Doroshenko, Vadym
Published: (2018)

Some combinatorial problems in the theory of partial transformation semigroups
by: Umar, A.
Published: (2018)

On monoids of monotone injective partial selfmaps of \(L_n\times_{\operatorname{lex}}\mathbb{Z}\) with co-finite domains and images
by: Gutik, Oleg, et al.
Published: (2018)