In this paper we prove the universal property of skew PBW extensions generalizing this way the well known universal property of skew polynomial rings. For this, we will show first a result about the existence of this class of non-commutative rings. Skew PBW extensions include as particular examples Weyl algebras, enveloping algebras of finite-dimensional Lie algebras (and its quantization), Art...

A large class of MDS linear codes is constructed. These are endowed with an efficient decoding algorithm. Both the definition and design their algorithm only require from Linear Algebra methods, making them fully accessible for everyone. Thus, first part paper develops a direct presentation by means parity-check matrices, rests upon matrix maps manipulations. The somewhat more sophisticated mat...

let $alpha$ be an endomorphism and $delta$ an $alpha$-derivationof a ring $r$.  in this paper we  study the relationship between an$r$-module $m_r$ and the  general polynomial module  $m[x]$ over theskew polynomial ring $r[x;alpha,delta]$. we introduce the notionsof skew-armendariz modules and skew quasi-armendariz modules whichare generalizations of $alpha$-armendariz modules and extend thecla...