Mathematica tools for quaternionic polynomials

In this paper we revisit the ring of (left) one-sided quaternionic polynomials with special focus on its zero structure. This area of research has attracted the attention of several authors and therefore it is natural to develop computational tools for working in this setting. The main contribution of this paper is a Mathematica collection of functions QPolynomial for solving polynomial problems that we frequently find in applications.(undefined)info:eu-repo/semantics/publishedVersio

N-products of modules and splitness

Let $$0 \longrightarrow \prod_{I}^{\aleph}M_{\alpha} \overset{\lambda}{\longrightarrow} \prod_{I}M_{\alpha} \overset{\gamma}{\longrightarrow} \operatorname{Coker}\lambda \longrightarrow 0$$ be an exact sequence of modules, in which $\aleph$ is an infinite cardinal, $\lambda$ the natural injection and $\gamma$ the natural surjection. In this paper, the conditions are given mainly in the four theorems so that $\lambda$ ($\gamma$ respectively) is split or locally split. Consequently, some known results are generalized. In particular, Theorem 1 of [7] and Theorem 1.6 of [5] are improved