We define skew matrix gamma ring and describe the constitution of Jordan left centralizers derivations on a -ring. also show properties these concepts.

Building on the work of K. Chiba (J. Algebra 263 (2003), 75– 87), we present sufficient conditions for the completion of a division ring with respect to the metric defined by a discrete valuation function to contain a free field, i.e. the universal field of fractions of a free associative algebra. Several applications to division rings generated by torsion-free nilpotent groups, skew Laurent se...

This thesis treats different kinds of standard bases in finitely generated modules over the ring of difference-skew-differential operators, their computation and their application to the computation of multivariate dimension (quasi-)polynomials. It consists of two parts. The first deals with standard bases in modules over the ring of difference-skew-differential operators. The second part deals...

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...

Abstract We show how a novel construction of the sheaf Cherednik algebras $\mathscr {H}_{1, c, X, G}$ on quotient orbifold $Y:=X/G$ in author’s prior work leads to results for G}$, which until recently were viewed as intractable. First, every orbit type stratum $X$, we define trace density map Hochschild chain complex generalizes standard Engeli–Felder’s differential operators {D}_X$. Second, b...

Let $R$ be a reversible ring which is $alpha$-compatible for an endomorphism $alpha$ of $R$ and $f(X)=a_0+a_1X+cdots+a_nX^n$ be a nonzero skew polynomial in $R[X;alpha]$. It is proved that if there exists a nonzero skew polynomial $g(X)=b_0+b_1X+cdots+b_mX^m$ in $R[X;alpha]$ such that $g(X)f(X)=c$ is a constant in $R$, then $b_0a_0=c$ and there exist nonzero elements $a$ and $r$ in $R$ such tha...

Empirical research on European stock markets has shown that they behave differently according to the performance of the leading financial market identified as the US market. A positive sign is viewed as good news in the international financial markets, a negative sign means, conversely, bad news. As a result, we assume that European stock market returns are affected by endogenous and exogenous ...

We give a new characterization of the bounded nilradical. Using the interplay between this and previous characterizations, we prove that the bounded nilradical is a graded ideal if the ring is graded. This allows us to completely determine the bounded nilradical of skew polynomial and skew Laurent polynomial rings in terms of information in the coefficient ring.