We classify the $\mathscr{R}$-cross-sections of the monoid of order-preserving transformations on the $n$-element chain in terms of certain binary trees.
Ramises Manzano, Jr., Gaudencio C. Petalcorin, Jr.
A pseudo hyper GR-algebra is an algebraic structure involving two distinct hyperoperations. Properties of this hyper algebra have been studied and given illustrations. This paper focuses on the quotient structure of pseudo hyper GR-algebras. From an equivalence relation on a pseudo hyper GR-algebra H, we can define a congruence relation on H that is used in the constructionof the quotient structure H/I, where I is the congruence class of 0 under the congruence relation. Moreover, some isomorphism theorems of pseudo hyper GR-algebras are included in this paper.
We survey a few of the many results now known about the self-distributivity law and selfdistributive structures, with a special emphasis on the associated word problems and the algorithms solving them in good cases.
The braids of $B\_\infty$ can be equipped with a selfdistributive operation $\mathbin{\triangleright}$ enjoying a number of deep properties. This text is a survey of known properties and open questions involving this structure, its quotients, and its extensions.
In this note we prove that the Chermak-Delgado lattice of a ZM-group is a chain of length $0$. A similar conclusion is obtained for all dihedral groups $D_{2m}$ with $m\neq 4$.