arXiv subjects

Daniel Birmajer

Publications and source records attributed to Daniel Birmajer.

21 records · Page 2Linked to original sources

arXiv2011

Factoring polynomials in the ring of formal power series over Z

We consider polynomials with integer coefficients and discuss their factorization properties in Z[[x]], the ring of formal power series over Z. We treat polynomials of arbitrary degree and give sufficient conditions for their reducibility as power series. Moreover, if a polynomial is reducible over Z[[x]], we provide an explicit factorization algorithm. For polynomials whose constant term is a prime power, our study leads to the discussion of p-adic integers.

math.AC↗

arXiv2004

Polynomial Detection of Matrix Subalgebras

It was proved by Giambruno-Sehgal and Chang that the double Capelli polynomial of total degree $4n$ is a polynomial identity for the algebra of n by n matrices over a field F. Using a strengthened version of this result obtained by Domokos, we show that the double Capelli polynomial of total degree 4n-2 is a polynomial identity for any proper matrix subalgebra. Subsequently, we present a similar result for nonsplit extensions of full matrix algebras.

math.RA↗

arXiv2003

On subalgebras of $n\times n$ matrices not satisfying identities of degree $2n-2$

The Amitsur-Levitski theorem asserts that $M_n(F)$ satisfies a polynomial identity of degree $2n$. (Here, $F$ is a field and $M_n(F)$ is the algebra of $n \times n$ matrices over $F$). It is easy to give examples of subalgebras of $M_n(F)$ that do satisfy an identity of lower degree and subalgebras of $M_n(F)$ that satisfy no polynomial identity of degree $\le 2n-2$. Our aim in this paper is to give a full classification of the subalgebras of $n \times n$ matrices that satisfy no nonzero polynomial of degree less than $2n$.

math.RA↗