In the year $1977,$ while developing the theory of modules arising in the context of Serre's problem on projective modules in the paper ``On Stably Free Modules"(see \cite{AS}), A. A. Suslin constructed matrices inductively using unimodular rows. Our aim is to connect these matrices to the current and applicable field...
Let $R$ be non-commutative ring with unity. In this paper, we prove that a given matrix in $M_n(R)$ is a sum of $p$-th powers in $M_n(R)$, where $n<p$ if and only if its trace can be written as a sum of $p$-th powers in $M_n(R)$, for $n = 2,3,4$ and $p = 5$ and $n = 4,5,6$ for $p = 7$. This paper extends the results of...
Jungin Lee in 2018 proved a necessary and sufficient condition that an integral quadratic form $\sum_{i=1}^{m} a_iX_i^2$ is universal over $M_2(\mathbb{Z})$. For a positive integer $n \geq 2$, Lee defined $f(n)$ to be the smallest positive integer $m$ such that for every pairwise coprime $a_1, a_2, \ldots a_m \in \math...
Mrunal Hardikar, A. S. Garge· 0 citations
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