Let A be an algebra over a commutative unital ring C. We say that A is zero triple product determined if for every C-module X and every trilinear map {·, ·, ·}, the following holds: if {x, y, z} 0 whenever xyz 0, then there exists a C-linear operator T : A3 −→ X such that {x, y, z} T xyz for all x, y, z ∈ A. If the ordinary triple product in the aforementioned definition is replaced by Jordan t...

We characterize finite, connected posets $P$ having a crown as retract. define multigraph $\mathfrak{F}(P)$ whose vertices are the so-called improper 4-crowns contained in extremal points of $P$, and we show that contains 4-crown retract iff there exists graph homomorphism certain type from to $\mathfrak{C}$ not depending on $P$. Additionally retract-crown with $n \geq 6$ poset induced by $n$ p...

‎let $mathcal{a}$ be a unital banach algebra‎, ‎$mathcal{m}$ be a left $mathcal{a}$-module‎, ‎and $w$ in $mathcal{z}(mathcal{a})$ be a left separating point of $mathcal{m}$‎. ‎we show that if $mathcal{m}$ is a unital left $mathcal{a}$-module and $delta$ is a linear mapping from $mathcal{a}$ into $mathcal{m}$‎, ‎then the following four conditions are equivalent‎: ‎(i) $delta$ is a jordan left de...

In this paper, we consider the hidden subgroup problem (HSP) over the class of semi-direct product groups Zn ⋊ Zq. The definition of the semi-direct product depending on the choice of an homomorphism, we first analyze the different possibilities for this homomorphism in function of n and q. Then, we present a polynomial-time quantum algorithm solving the HSP over the groups of the form Zpr ⋊ Zp...