Necessary and sufficient conditions for an Ore extension S = R[x;σ, δ] to be a PI ring are given in the case σ is an injective endomorphism of a semiprime ring R satisfying the ACC on annihilators. Also, for an arbitrary endomorphism τ of R, a characterization of Ore extensions R[x; τ ] which are PI rings is given, provided the coefficient ring R is noetherian.

Given a finite group G acting as automorphisms on a ring A, the skew group ring A∗G is an important tool for studying the structure of G-stable ideals of A. The ring A∗G is G-graded, i.e.G coacts on A∗G. The Cohen-Montgomery duality says that the smash product A ∗ G#k[G]∗ of A ∗ G with the dual group ring k[G]∗ is isomorphic to the full matrix ring Mn(A) over A, where n is the order of G. In th...

Density functional theory (UB3LYP/6-31G(d,p)) was used to determine substituent effects on the singlet-triplet-state energy gap for 21 meta-substituted phenylnitrenium ions. It was found that strongly electron-donating substituents stabilize the triplet state relative to the singlet state. With sufficiently strong meta electron donors (e.g., m,m'-diaminophenylnitrenium ion) the triplet is predi...

Three types of equations of mathematical physics, namely, the equations, which describe any physical processes, the equations of mechanics and physics of continuous media, and field-theory equations are studied in this paper. In the first and second case the investigation is reduced to the analysis of the nonidentical relations of the skew-symmetric differential forms that are obtained from dif...

In this work, cyclic-skew-cyclic codes and sum-rank BCH are introduced. Cyclic-skew-cyclic characterized as left ideals of a suitable non-commutative finite ring, constructed using skew polynomials on top (or vice versa). Single generators such found, they used to construct generator matrices the corresponding codes. The notion defining set is introduced, pairs roots poynomials. A lower bound (...

For every ring R, we construct a ringed space NCSpec(R) and for every ring homomorphism R → S, a morphism of ringed spaces NCSpec(S) → NCSpec(R). We show that this gives a fully faithful contravariant functor from the category of rings to a category of ringed spaces. If R is a commutative ring, we show that NCSpec(R) can be viewed as a natural completion of Spec(R). We then explain how the spac...