6 papers · 1 filter
Roots of polynomials over semirings and hyperfields
Louis Halle Rowen
We continue our investigation of roots of polynomials over semirings and hyperfields, employing a property on semiring and hyperfield ``pairs'' with a surpassing relation $\preceq,…
Makar-Limanov's problem on values of polynomials on matrices
Louis H. Rowen, Uzi Vishne
Suppose is an infinite field and let be a noncommutative polynomial. Partially answering a query of Makar-Limanov, we show that there are numbers $d…
Tensor products of bimodules over monoids
Louis H. Rowen
We modify the well-known tensor product of modules over a semiring, in order to treat modules over hyperrings, and, more generally, for bimodules (and bimagmas) over monoids. The t…
Axial identities
Louis Halle Rowen
The notions of idempotental identities and axial identities of axial algebras are introduced, in order to understand better some theorems of J.~Desmet, I.~Gorshkov, S.~Shpectorov,…
Frobenius forms on weakly primitive axial algebras of Jordan type
Louis Rowen, Yoav Segev
In a previous paper we studied ``weakly primitive axial algebras'' with respect to more general fusion rules, for which at least one axis satisfies the fusion rules. In this contin…
Weakly primitive axial algebras
Louis Halle Rowen, Yoav Segev
In earlier work we studied the structure of primitive axial algebras of Jordan type (PAJ's), not necessarily commutative, in terms of their primitive axes. In this paper we weaken…