7 papers
Roots of polynomials over semirings and hyperfields
Louis Halle Rowen
We lay the groundwork for the theory of roots of polynomials over semirings and hyperfields, employing a property of a ``surpassing relation'' on semirings and hyperfield…
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…
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…
Axial identities
Louis Halle Rowen
Axial algebras are algebras generated by semisimple idempotents whose eigenspace decompositions satisfy prescribed fusion rules, such as Jordan fusion rules, which hold in Jordan a…
Tensor products of bimodules and bimodule pairs over monoids
Louis H. Rowen
We modify the well-known tensor product of modules over a semiring, to provide a general theory encompassing the classical theory of tensor products over algebras, tropical structu…
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…
Residue Structures
Louis H. Rowen
We consider residue structures where is an additive subgroup of a ring , not necessarily an ideal. Special instances include Krasner's construction of qu…