AbstractLet Fn be the ring of n × n matrices over the finite field F; let o(Fn) be the number of elements in Fn, and s(Fn) be the number of singular matrices in Fn. We prove that o(Fn)<s(Fn)1+1n(n-1) if n ⩾ 2, and if n = 2 and o(F) ⩾ 3, then s(Fn)1 + 1n2<o(Fn)<s(Fn)1+1n(n-1)
Let $K$ be a number field and ${\mathcal O}$ be the ring of $S$-integers in $K$. Morgan, Rapinchuck,...
We find bounds for the number of idempotents in a ring of matrices over an arbitrary finite commutat...
AbstractThe probability that the product of l square matrices of size n over a finite field with q e...
AbstractLet Fn be the ring of n × n matrices over the finite field F; let o(Fn) be the number of ele...
AbstractThe probability that the product of l square matrices of size n over a finite field with q e...
This project was submitted to the Mathematics department in partial fulfillment of the requirements ...
AbstractWe show that for any subset E⊆Fqd with |E|≫qd−1+2d, the number of singular matrices whose ro...
We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite...
AbstractLet F be a field, char(F)≠2, and S⊆GLn(F), where n is a positive integer. In this paper we s...
AbstractLet F be a field, char(F)≠2, and S⊆GLn(F), where n is a positive integer. In this paper we s...
AbstractWe use an upper bound on the number of zeros of sparse polynomials over a finite field Fq to...
AbstractLet F=GF(q) denote the finite field of order q, and Fmn the ring of m×n matrices over F. Let...
AbstractThe authors determine the number of (n+m)×t matrices A∗ of rank r+v, over a finite field GF(...
AbstractLet Zm denote the ring of integers modulo m, and let (Zm)n denote the complete ring of all n...
AbstractLet Fn denote the ring of n×n matrices over the finite field F=GF(q) and let A(x)=ANxN+ ⋯+ A...
Let $K$ be a number field and ${\mathcal O}$ be the ring of $S$-integers in $K$. Morgan, Rapinchuck,...
We find bounds for the number of idempotents in a ring of matrices over an arbitrary finite commutat...
AbstractThe probability that the product of l square matrices of size n over a finite field with q e...
AbstractLet Fn be the ring of n × n matrices over the finite field F; let o(Fn) be the number of ele...
AbstractThe probability that the product of l square matrices of size n over a finite field with q e...
This project was submitted to the Mathematics department in partial fulfillment of the requirements ...
AbstractWe show that for any subset E⊆Fqd with |E|≫qd−1+2d, the number of singular matrices whose ro...
We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite...
AbstractLet F be a field, char(F)≠2, and S⊆GLn(F), where n is a positive integer. In this paper we s...
AbstractLet F be a field, char(F)≠2, and S⊆GLn(F), where n is a positive integer. In this paper we s...
AbstractWe use an upper bound on the number of zeros of sparse polynomials over a finite field Fq to...
AbstractLet F=GF(q) denote the finite field of order q, and Fmn the ring of m×n matrices over F. Let...
AbstractThe authors determine the number of (n+m)×t matrices A∗ of rank r+v, over a finite field GF(...
AbstractLet Zm denote the ring of integers modulo m, and let (Zm)n denote the complete ring of all n...
AbstractLet Fn denote the ring of n×n matrices over the finite field F=GF(q) and let A(x)=ANxN+ ⋯+ A...
Let $K$ be a number field and ${\mathcal O}$ be the ring of $S$-integers in $K$. Morgan, Rapinchuck,...
We find bounds for the number of idempotents in a ring of matrices over an arbitrary finite commutat...
AbstractThe probability that the product of l square matrices of size n over a finite field with q e...
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