Abstract In this text, we will show the existence of lattice packings in a family dimensions by employing division algebras. This construction is generalization Venkatesh’s packing result Venkatesh (Int Math Res Notices 2013(7): 1628–1642, 2013). our construction, replace appearance cyclotomic number field with algebra over rational field. We employ probabilistic argument to lattices certain go...

In this paper $n$-ary regular division algebras are discussed, which satisfying the hyperidentity of paramediality. It is shown that every operation in paramedial algebra will be linearly represented over same Abelian group. Similar results already obtained for medial [1].