in this paper we consider the solutions of linear systems of saddle point problems‎. ‎by using the spectrum of a quadratic matrix polynomial‎, ‎we study the eigenvalues of the iterative matrix of the hermitian and skew hermitian splitting method‎.

‎‎A natural generalization of two dimensional cyclic code ($T{TDC}$) is two dimensional skew cyclic code‎. ‎It is well-known that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring $R_n:=F[x,y;rho,theta]/_l$‎. ‎In this paper we characterize the left ideals of the ring $R_n$ with two methods and find the generator matrix for two dimensional s...

In this paper we prove the universal property of skew PBW extensions generalizing this way the well known universal property of skew polynomial rings. For this, we will show first a result about the existence of this class of non-commutative rings. Skew PBW extensions include as particular examples Weyl algebras, enveloping algebras of finite-dimensional Lie algebras (and its quantization), Art...

Abstract: In this paper, we consider the skew circulant and skew left circulant matrices with the Fibonacci and Lucas numbers. Firstly, we discuss the invertibility of the skew circulant matrix and present the determinant and the inverse matrix by constructing the transformation matrices. Furthermore, the invertibility of the skew left circulant matrices are also discussed. We obtain the determ...

In this paper we consider the solutions of linear systems of saddle point problems‎. ‎By using the spectrum of a quadratic matrix polynomial‎, ‎we study the eigenvalues of the iterative matrix of the Hermitian and skew Hermitian splitting method‎.

In analogy to cyclic codes, we study linear codes over finite fields obtained from left ideals in a quotient ring of a (non commutative) skew polynomial ring. The paper shows how existence and properties of such codes are linked to arithmetic properties of skew polynomials. This class of codes is a generalization of the θ-cyclic codes discussed in [1]. However θ-cyclic codes are performant repr...

In this paper, amodulus-based generalized skew-Hermitian triangular splitting (MGSTS) iteration method is present for solving a class of linear complementarity problems with the system matrix either being an H+-matrix with non-positive off-diagonal entries or a symmetric positive definite matrix. The convergence of the MGSTS iterationmethod is studied in detail. By choosing different parameters...

Recommended by Francois Goichot In this article, we study the relationship between left right zip property of R and skew polynomial extension over R, using the skew versions of Armendariz rings.

In this survey paper we define partial actions of groups on algebras and give several related results. For any partial action a partial skew group ring is defined. This partial skew group ring is not always associative. Conditions under which associativity holds are studied. Several other questions are considered like, for example, enveloping actions and properties of partial skew group rings.