in this paper we define the notions of ultra and involution ideals in bck-algebras. then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. specially, we show that in a bounded implicative bck-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower bck-semilattice, the notions of...

An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R.

This paper aims to investigate properties of strictly involution binary relations, which are generalizations of the classical notions of binary relations. We study the concepts of involution spanning subsets and give some examples related to different involution binary relations. Moreover, the involution independence with code is also considered in this paper.

There is a natural involution on Christoffel words, originally studied by the second author in [dL2]. We show that it has several equivalent definitions: one of them uses the slope of the word, and changes the numerator and the denominator respectively in their inverses modulo the length; another one uses the cyclic graph allowing the construction of the word, by interpreting it in two ways (on...

Let Modg be the modular group of surfaces of genus g. Each element [h] ∈ Modg induces in the integer homology of a surface of genus g a symplectic automorphism H([h]) and Poincaré shown that H : Modg → Sp(2g,Z) is an epimorphism. The theory of real algebraic curves justify the definition of real Riemann surface as a Riemann surface S with an anticonformal involution σ. Let (S, σ) be a real Riem...

Let $A$ be an associative algebra over a field of characteristic zero. A central polynomial is the free that takes values $A.$ In this survey, we present some recent results about exponential growth codimension sequence and proper in setting algebras with involution graded by finite group.

We present an algorithm to reduce the constructive membership problem for a black-box group G to three instances of the same problem for involution centralisers in G. If G is a simple group of Lie type in odd characteristic, then this reduction can be performed in (Monte Carlo) polynomial time.

In this article, we introduce a kind of unitary operator U associated with the involution on the Heisenberg group, invariant closed subspaces are identified with the characterization spaces of sub-Laplacian operators. In the sense of vector-valued functions, we study the theory of continuous wavelet transform. Also, we obtain a new inversion formula of Radon transform on the Heisenberg group Hn.