Canonical orders, introduced in the minimal model program for orders [CI05], are simultaneous generalisations of Kleinian singularities k[[s, t]], G < SL2 and their associated skew group rings k[[s, t]]∗G. In this paper, we construct minimal resolutions of canonical orders via non-commutative cyclic covers and skew group rings. This allows us to exhibit a derived equivalence between minimal res...

A Leavitt labelled path algebra over a commutative unital ring is associated with space, generalizing algebras graphs and ultragraphs as well torsion-free generated by idempotents. We show that can be realized partial skew group rings, Steinberg algebras, Cuntz-Pimsner algebras. Via these realizations we obtain generalized uniqueness theorems, description of diagonal preserving isomorphisms cha...

Let R = K[x;σ] be a skew polynomial ring over a division ring K. We introduce the notion of derivatives of skew polynomial at scalars. An analogous definition of derivatives of commutative polynomials from K[x] as a function of K[x] → K[x] is not possible in a non-commutative case. This is the reason why we have to define the derivative of a skew polynomial at a scalar. Our definition is based ...

In this paper, it has been proved that for a Noetherian ring R and an automorphism σ of R, an associated prime ideal of R[x, σ] or R[x, x−1, σ] is the extension of its contraction to R and this contraction is the intersection of the orbit under σ of some associated prime ideal of R. The same statement is true for minimal prime ideals also. It has also been proved that for a Noetherian Q-algebra...

We study the BGG Category O over a skew group ring, involving a finite group acting on a regular triangular algebra. We relate the representation theory of the algebra to Clifford theory for the skew group ring, and obtain results on block decomposition, semisimplicity, and enough projectives. O is also shown to be a highest weight category; the BGG Reciprocity formula is slightly different bec...

In previous works we considered codes defined as ideals of quotients of non commutative polynomial rings, so called Ore rings of automorphism type. In this paper we consider codes defined as modules over non commutative polynomial rings, removing therefore some of the constraints on the length of the codes defined as ideals. The notion of BCH codes can be extended to this new approach and the c...