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Publications (5)

math.RA2025

Counterexamples in Involutions of Azumaya Algebras

Uriya First, Ben Williams

Suppose $A$ is an Azumaya algebra over a ring $R$ and $I ¨ $ is an involution of $A$ extending an order- $2$ automorphism $I^» : R \to R$ . We say $I ¨ $ is extraordinary if there does not e…

cs.CC2026

Good Locally Testable Codes with Small Alphabet and Small Query Size

Uriya First, Stav Lazarovici

Ben-Sasson, Goldreich and Sudan showed that a binary error correcting code admitting a $2$ -query tester cannot be good, i.e., it cannot have both linear distance and constant rate.…

math.RA2025

Irredundant Generating Sets for Matrix Algebras

Yonatan Blumenthal, Uriya First

Let $F$ be a field. We show that the largest irredundant generating sets for the algebra of $n \times n$ matrices over $F$ have $2 n - 1$ elements when $n > 1$ . (A result of Laffey stat…

math.NT2017

On the number of generators of a separable algebra over a finite field

Uriya First, Zinovy Reichstein, Santiago Salazar

Let $F$ be a field and let $E$ be an Ã©tale algebra over $F$ , that is, a finite product of finite separable field extensions $E = F_{1} \times \dots \times F_{r}$ . The classical primit…

math.SP2020

A spectral theory for transverse tensor operators

Uriya First, Joshua Maglione, James B. Wilson

Tensors are multiway arrays of data, and transverse operators are the operators that change the frame of reference. We develop the spectral theory of transverse tensor operators an…