On Edge Q-algebras (European Journal of Pure and Applied Mathematics, 2025)
The concept of an edge in Q-algebra is introduced in this work. We explore some properties of edge Q-algebras. The characterization of subsets of an edge Q-algebra to be subalgebras is provided. We show that for an edge Q-algebra X of order n, there are 2n-1 subalgebras of X.  Moreover, the set of all subalgebras forms a semigroup with a right identity. Beside this, the concept of ideal is discussed. We obtain that the set of all ideals forms a left zero semigroup and a simple semigroup. Finally, we describe all possible structures of edge Q-algebras and enumerate all members of a class of all edge Q-algebras.  We prove that there are exactly 2n^2-3n+2 edge Q-algebras of order n. Finally, we show a connection between Q-algebras and d-algebras. We obtain that every edge d-algebra is a Q-algebra. Precisely, every edge d-algebra is an edge Q-algebra.
Keywords: Q-algebra; subalgebra; ideal; edge; edge Q-algebra; semigroup