Reduction relations are means to express congruences on rings. In the special case of congruences induced by ideals in commutative polynomial rings, the powerful tool of Grabner bases can be characterized by properties of ...

Ore extensions (introduced by Ore [33]) have been one of the most studied non-commutative structures in the last century. The skew polynomial rings (see Definition 1.1.1) are an Ore extensions that thanks to its similarity ...

This is the first of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida ...

We introduce the notion of non commutative truncated polynomial extension of an algebra A. We study two families of these extensions. For the first one we obtain a complete classification and for the second one, which we ...

In this document we review the notion of Hopf Galois extensions, addressing remarkable examples, some properties and recent advances in such theory. Similarly, we present some families of non-commutative rings and algebras ...

Abstract. We study some relations and interactions between non-commutative algebraic geometry and the skew PBW extensions. For this we will introduce a new class of noncommutative rings, the semi-graded rings, and for ...

Many rings and algebras arising in quantum mechanics, algebraic analysis, and non-commutative algebraic geometry can be interpreted as skew PBW (Poincare- Birkhoff Witt) extensions. In the present paper we study two aspects ...