The endomorphism monoid of a free trioid of rank 1

Structure of relatively free trioids

“…The trioid (F ′ , ≺, ≻, ↑) was also considered in [35]. Another representation of the free trioid of rank 1 can be found in [16].…”

“…In [34], it was proved that endomorphism semigroups of free trioids are isomorphic if and only if the corresponding free trioids are isomorphic. The endomorphism monoid of the free trioid of rank 1 was studied in [35].…”

Free abelian trioids

“…Later, it was shown that the free trioid of an arbitrary rank has the similar structure (see [20,28]). More convenient isomorphic constructions of the free monogenic trioid and the free trioid of an arbitrary rank were proposed in [30] and [19], respectively. Besides, in [30] the endomorphism monoid of the free trioid of rank 1 was described (see also the case for dimonoids of rank 1 [31]).…”

“…More convenient isomorphic constructions of the free monogenic trioid and the free trioid of an arbitrary rank were proposed in [30] and [19], respectively. Besides, in [30] the endomorphism monoid of the free trioid of rank 1 was described (see also the case for dimonoids of rank 1 [31]). The structure of free commutative trioids and other relatively free trioids was presented in [15,18].…”

On automorphisms of the semigroup of endomorphisms of a free abelian dimonoid

“…It is not hard to see that a dimonoid becomes a semigroup if the operations of a dimonoid coincide. Dimonoids play a prominent role in the theory of Leibniz algebras, these structures and related systems have been studied by many authors (see, e.g., [2] [5]).…”