If [Formula: see text] is a directed graph and field, the Leavitt path algebra of over naturally graded by group integers We formulate properties which are equivalent with being crossed product, skew ring, or ring respect to this natural grading. state main result so that also characterized in terms pre-ordered Grothendieck text]-group text]. has finitely many vertices, we characterize when str...

Abstract Let S be a domain and R = [ t ; σ, δ ] skew polynomial ring, where σ is an injective endomorphism of left -derivation. We give criteria for polynomials f ∈ degree less or equal to four irreducible. apply them low in quantized Weyl algebras the quantum planes. also consider ( ) m − .

A ring $R$ is called a left Ikeda-Nakayama (left IN-ring) if the right annihilator of intersection any two ideals sum annihilators. As generalization IN-rings, SA-ring annihilators an ideal $R$. It natural to ask IN and SA property can be extended from $R[x; \alpha, \delta]$. In this note, results concerning conditions will allow these properties transfer skew polynomials $R[x;\alpha,\delta]$ a...

We give a practical criterion characterizing the monogenicity of the integral closure of a Dedekind ring R, based on results on the resultant Res(P,Pi) of the minimal polynomial P of a primitive integral element and of its irreducible factors Pi modulo prime ideals of R. We obtain a generalization and an improvement of the Dedekind criterion (Cohen, 1996) and we give some applications in the ca...

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...

The molecular structure and conformational composition of (silylmethyl)cyclopropane (SMCP), C3Hs-CH2-SiH3, with respect to the Cring-CH 2 and the CH2-Si axes have been studied by gas-phase electron diffraction and ab initio calculations using a 6-31 G* basis set. The conformational analysis, with respect to the Cring-C bond, has shown that the gauche (skew) form is the predominant conformation ...

An significant milestone study in coding theory recognized to be the paper written by Hammons at al. [1]. Fields are useful area for constructing codes but after the study [1] finite ring have received a great deal of attention. Most of the studies are concentrated on the case with codes over finite chain rings. However, optimal codes over nonchain rings exist (e.g see [2].) In [3], et al. stud...

When a finite group acts linearly on a complex vector space, the natural semi-direct product of the group and the polynomial ring over the space forms a skew group algebra. This algebra plays the role of the coordinate ring of the resulting orbifold and serves as a substitute for the ring of invariant polynomials from the viewpoint of geometry and physics. Its Hochschild cohomology predicts var...